They have always stored the private keys in their database but only encrypted.
Basically when you create a wallet, your keys are generated in your browser then they are encrypted in your browser then sent to their servers to be stored there. Each time you login you then fetch the encrypted keys, decrypt them in your browser and use them there.

This way they won't have access or control over your keys (hence non-custodial) but still you are storing the keys remotely in a server that could be hacked and maybe there could be some vulnerabilities in the way they encrypt the keys which could be exploited to steal your coins!

The thing is that you can never "win" this thing ever. And adding a "history" would require storage and dedicated hosting which I don't think there is any way you could do it using github pages. On top of that turning this to something that starts looking more like a lottery and involving tips is going to break a bunch of github terms.

You already answered your question. Source of your funds are "legit" in "your" eyes not in the eyes of some centralized custodial wallet. They can some day decide that the funds you received (for example from a gambling signature campaign) were not "legit" and shut down your account, effectively never letting you get your bitcoins out.
Gambling is just an example, there are lots of things that could go wrong. For example you may deal with a business that is outside of US and some day US decides that the said jurisdiction is evil and orders Coinbase etc to cut ties and shut down accounts of anybody from there or dealing with people there.

It is only complicated for those who have no idea how bitcoin and specifically blocks and mining them works. Otherwise the only difference between Genesis block and any other block is that Genesis block's previous block hash is empty! Everything else is the same.

I said it already in third paragraph above. There are lots of deposits too where users send their bitcoins to exchanges. That doesn't have anything to do with bull or bear market though, when price goes up some people sell, some people buy. Same as when price goes down and the fees go up all the same.

We still haven't reached 2017 fee levels. A lot of blocks during 2017 had a total of 10 to 14BTC total fees for miners and those blocks were smaller than today's blocks too. These days the total fee of the blocks for "high" fees reach between 1.8 to 2.2BTC for each block.

The reason why you think they are "higher" is because bitcoin price in 2017 was between $900 and $20,000 but today the price is $55,000. Meanwhile we are still paying the same satoshis for the same amount of bytes.

A paper wallet is simply a "secret" that is written on a physical medium including but not limited to paper.
That secret can be your private key, your mnemonic or your password,... and the security of it depends on (1) how it was created (2) how it was printed and (3) how it is stored.

Obviously if you create the paper wallet using a website and do it on a possibly compromised computer and store it recklessly then it is going to be the least safe thing to do!
But you could generate it on an airgap computer using a safe software such as an open source and trusted desktop wallet (eg. Electrum) and store the key encrypted and create multiple backups of it. This way it can be the safest option.

Isn't it obvious?
When the user makes a withdrawal request, they want to receive their bitcoins in whatever destination it has, as soon as possible. So the exchange has to pay high priority fee or their support staff are going to be flooded with angry tickets and their reputation is screwed.
Similarly when the user makes a deposit, they want the coins to be confirmed as soon as possible so that they can use them right away.

When there is less space compared to users (low supply, high demand) the fee (cost of that space) goes up due to the intense competition for that space.
This is why we need to scale main-chain more and we need exchanges to move to LN sooner.

This chart is nothing because it has no time-frame and no values on it. It doesn't even have a title indicating what asset this chart belongs to, we are assuming this is bitcoin since this is bitcoin speculation board.
You can't decide if the market is bullish or bearish based on this zoomed in chart!

THIS is the daily chart spanning around 6 months or so not the one you posted, and THIS is bullish, and a very healthy one at that too:

That may be a small reason at this point but the main reason is that using LN doesn't make sense here. LN is useful if you are going to send/receive multiple payments with the channel you open. But if it is a one time payment every week/month then it makes no sense and it also costs more than the on-chain transaction.

Lets say your signature campaign wanted to do this, they have to:
1. Open a channel for this week/month 's payment which means sending an on-chain transaction to that channel (fee #1)
2. Send out the payment to each user on LN (a tiny LN fee for each tx)
3. Close the channel since there won't be any payment until next round (fee #2)
4. Each user (or at least most of them) that receives the payment has to close their channel and move the coins to their wallets (fee #3)
This means using LN in this case replaced 1 on-chain fee with 3 on-chain and a tiny LN fees which makes no sense.

This is only true for bitcoin and possibly some of the popular altcoins that have open source and reviewed desktop (and other type of) wallets but not for majority of tokens and shitcoins.
I'd argue that storing the later in exchanges is a lot safer than installing a shady closed source wallet that nobody has reviewed and can contain malware. You can end up trying to save the shittoken but lose your bitcoin after installing the shittoken's wallet.

There is also the problem with the pump and dump nature of the altcoins which demands storage on exchanges for quick access so that you can dump them fast or risk losing all the profit that was gained in the pumping stage.

Since the keys are derived using a hash function and there is no relationship between the input of the hash function and the output of it, there is also no relationship between the master key and each child key that is derived from it that could be "exploited".

Each depth can have an index from 0 to 0xFFFFFFFF which is 4.2 billion. Even the most common paths used by wallets is still a huge list. It is not possible "to derive all paths".

This is a good idea but there is a much easier workaround method. You simply create the transaction you want to send and sign it BUT don't send/broadcast it to network. Instead copy it as raw bytes (or hex) and use any decoder online to count the bytes. You can do it manually too, count hex characters and divide it by two. Now you know what your transaction "byte" size is so you can set the fees accurately.

If you are using Electrum or bitcoin core or any other wallet that copies the core behavior you don't need the following:
You should add 1 byte per input since there is a small chance your signatures may vary in size (be bigger by 1 or 2 bytes).

When you sign the second transaction (with higher fee of 10 sat/byte) you should double check the size and your fee before broadcasting.

Wrong.
The high fees is a combination of bitcoin being actually used up to its max capacity and more, plus the price suddenly making a big move in any direction that causes a lot of people moving their coins to and from exchanges (something altcoin bag holders never do since they mostly keep it on exchanges) and the recent drop in hashrate.
In altcoins due to lack of utility they remain unused unless they spam their own chain with useless transactions like what ethereum does with all the garbage ICO spam. So their blocks remain empty for the most part and their fees rarely go up. Additionally most of them have fundamental flaws that if there is an increased on-chain traffic their network could simply go down as all nodes crash.

You question is wrong because there is a huge difference between bitcoin market and altcoin market so you can't just ask about "cryptocurrency market" as a whole.

Bitcoin prices were already rising and high when Elon Musk started the hype and it didn't really affect the price since the trend didn't change if you zoom out and look at the chart over the longer period than the single day he hyped it up on Twitter.

On the other hand the Dogecoin price wasn't doing anything and it was already dumping but when Musk started hyping it up its price started pumping hard.  You can clearly see that on its charts if you zoom out similar to what you did to bitcoin charts.
In a little while when the hype is over Doge will dump again while bitcoin continues going up.

So you see there is a huge difference between the two.

"Invest" in a stablecoin? That's new and dumb

Crash is if price reached $40k level. This was small drop that could even be considered a correction although I call it a manipulation.

I don't think so. People who wanted to buy bitcoin have been doing it already regardless of what Chinese bank says and anyone who hasn't already is unlikely to start because of this news specially since there is no Chinese bitcoin exchange left inside China since they closed them all down for illegal activities a couple of years ago.

Centralized exchanges are just a place where different "people" meet to trade with each other and the exchange only provides the server and security and gets paid for that when they receive the trading fees for each trade you make.

As I said you are paying for the service they provide.

Considering the fact that when you deposit money or bitcoin into your exchange account you are giving the exchange full control of those funds the answer is yes.

The real question you have to ask yourself is how much potential for growth you see in what you are buying.

Bitcoin has a lot of potential, it still hasn't been adopted more than 1 to 2% and there is a long way to go to reach mass adoption. And most importantly bitcoin is a useful currency that is offering a very unique utility (censorship resistance payment system). So it will continue to grow.

Comparing that with altcoins, I personally don't see any long term potential in any of the altcoins. Majority of them either have no new ideas or are seriously broken. That is why most of them are only alive to be pumped and dumped.

Yes assuming there are other keys derived from that master key and assuming that the derived key that was found by "super luck" was not the result of a collision.

Since the actual finalized code for Taproot activation was added recently there isn't any other completed implementation of it available, that includes Electrum and Hardware wallets. We have to first wait for them to implement these new features and see them extensively be tested then be used with real bitcoins.
Then you'll have to both create a new wallet and transfer your bitcoins using an on-chain transaction to that new wallet to be able to use the new features.

Whats up with all these broken English FUD topics today on bitcointalk?
It looks like the new wave of newbie FUDsters trying their hand on spreading FUD. At least in the past they used to put some effort into their FUD and write more than one line and with better English. Now it is just lazy throwaway accounts that write these idiotic FUD titles that give you a headache to read.