I would love to participate on this campaign. I would love to hear from you.

Your Username: Ctstrphy
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Your BTC Address: 1C9ACJLsNeWPs1obXzKDSNpkNY4kW82MpV

Let's clear this up since the responses here seem a bit confusing.

With online wallets that you sign up to, you are not sending the transactions, they are.  Therefore they have control over what fees you pay, however all of the fees are going to the miners.

The fees which the online wallet will be paying for your transaction will either be the same as a normal transaction like blockchain.info, or in the case of some providers they will group together several transactions into one transaction (a batch transaction) to lower the amount of fees they have to pay overall due to lower transaction sizes in bytes.  If they offer it for free, they're probably doing this along with their own methods of earning profit from running the wallet so that they can cover your costs themselves.

Electrum is a "real" wallet.  That means that you are sending the transactions.  When you're doing it, you have responsibility over the fees you pay.  The fees which will result in a quick confirmation do not rely on the wallet - sending from a hardware wallet, a software wallet (like Electrum) or any other wallet which you actually own yourself will only rely on the size of the transaction.

The main thing that determines the size of the transaction is the number of inputs and outputs in the transaction.  If you accept 1 Bitcoin three times and then you send a 3 Bitcoin transaction, that 3 Bitcoin transaction will have 3 inputs.  The more inputs, the higher your fees will be.  Outputs are just what addresses you're sending to, so your fees would then be higher if you were doing a batch transaction as well.  There are other factors which are why batch transactions are cheaper, but these are the main factors that you can control.

That's part of the reason why faucets are a waste of time - if you accept too many payments, your fees will get nearly as high as your amount of Bitcoin.  The only way to remedy the insane fees are to use faucet caches which hold the Bitcoin until you have a high enough amount to withdraw, but it'll take a long time because faucets are still just paying dust anyway.

1. The algorithms used to calculate the fees differs from one wallet to another. If they are the same then It's because of the transaction size (satoshis/bitcoins-per-kilobyte) and sometimes, third party wallets take a fee for themselves. If the wallet you are using allow changing the fees then I suggest taking a look here: https://bitcoinfees.21.co/ to know what's the best/slowest/fastest etc.

2. Hardware wallets are no different from other wallets when It comes to the fees. If by "bit by bit" you mean receiving a few satoshis from faucets etc... then that's not recommended yes.

3. I believe Electrum allow dynamic fees but I'm not sure, download the latest version and check by yourself.

some wallet automatically computes the best range of fee so your transaction will not be stucked while some wallet have a standard fee of .0002 or 0.0003 for every transaction.
I use electrum now and transaction fee requires 0.0003+ btc . It depends on the amount you are sending but I think this is already cheaper compared to other wallet I use because it's already with highest priority compared to other wallet which costs me upto 0.0006 btc per transaction.

Mining equipment is just specialized hardware to solve the mining problem. Different altcoins use different algorithms and may require different hardware which is why Bitcoin ASICs won't work a lot of altcoins.

Designing your own mining hardware is a large undertaking and won't be easy unless you just plan to make a PC with a bunch of GPUs to do some altcoin mining.