Is Ethereum really slower than Bitcoin? I've just looked up number of pending transactions, ethereum has 22000-23000, bitcoin has +216000

not really sure I fully understand the example you've given there.

If you use economic theory, price is worked out using supply and demand so in theory, you can fix the market value of something by constantly adjusting the supply to always meet demand. You might be able to use formulae used for estimating velocity of money to create an algorithm for estimating exactly what the change in supply needs to be. Manipulating supply won't be perfect as you'd have to wait maybe a few weeks between the supply being adjusted and market forces reacting to it but it could give long term price stability.

You could also have the currency look up the sales value on exchanges and adjust the supply to push it's value towards the optimum but this relies on exchanges which means it can be indirectly manipulated by someone messing up the price on the exchange.

I think you'd have to have potentially infinite inflation when prices are too high and some mechanism that encourages saving when prices are too low, or a system that creates new coins when prices are too high and incentivizes users to destroy coins when prices are low, maybe something like have two currencies (coins and shares) where users can trade coins for shares but can't turn shares back into coins (so coins get taken out of circulation whenever shares are purchased = deflation) and then have a proof-of-stake system where users with the most shares can "win" and get paid in coins.

the problem with what you've proposed here is that whilst you can expand the supply of coins when demand goes up, you can't reduce the supply of coins when demand goes down (not to say supply can't be reduced, just what's been suggested here doesn't imply that it can).

I did once try running some calculations on a hypothetical coin that would delete coins used in transaction fees and use variable block rewards to keep volume at a fixed rate but the problem is that cryptocurrencies regularly go up or down 25% per week, so you'd have to reduce the supply of coins by a huge amount whenever demand drops. the only way this hypothetical currency would work is either have ridiculously high transaction fees or run the risk of constantly devaluing itself too much. Decreasing the value of each individual coin is fairly easy but increasing the value is much harder.

If you wanted a centralized currency that increases in value, you could copy tether (central exchange buys and sells coins at a fixed value) but use something like transaction fees to slowly reduce the supply and push the central exchange price up accordingly but this would only be as much increase in price as there is decrease in coins so higher transaction fees would be needed for higher growth in value.

It seems like their was a similar thing done to increase bitcoin nodes although it look like they stopped once they reach 10000 nodes. Link
Although it would be very useful for smaller altcoins as a way of spurring early growth in their networks.

So for example, you could have rewards for solving blocks, but the also have another smaller reward that goes to anyone who is running a full node. this would create an incentive to people to keep their nodes runing even if their device has low hashpower

right now, im thinking about designing an altcoin that uses both PoW to mine and then uses something like PoS, where everytime a block gets enough confirmations to be added to the blockchain, one of the nodes that was online when the block was made, is picked at random and given a small reward (although nodes with higher stake would have better chance of winning). maybe it should be called "proof of node"? People mining this coin would get to choose between PoW, which requires hashpower, or PoN, which doesnt

are there any problems with this idea?

EDIT: changed incorrect terminology