My question : is Bitcoin spendable in the first place ? Is it designed for and only for HODL, to provide a proof of wealth/stake ?
Yes, bitcoin is a currency and can be spent. Bitcoin is all in all, it is also an asset.
The second : I always heard the "be your own bank" among crypto features. Will the next step is to be your own CENTRAL bank ?
The statement to be your own bank means you can independently save bitcoin on your own without depending on third parties generally, not only banks, but also not depending on exchanges and others but you to have your private key which makes this a reality.
By this, should there be a feeless coin where every person holding some BTC (say 0.01) can issue its coin which should have a total market cap equivalent to his holding in BTC ?
There are coins like that, but not everyone will hold their different coin because the value in a coin is its marketcap, if a coin is not supported by people buying it, it will remain a worthless coin.