To lessen possible damage, better secure your funds in your own wallet. Once you finished trading, store your funds in your own wallet.
While good advice, the caveat with this is that there are plenty of exchanges out there which will let you open an account, complete KYC, deposit funds, trade those funds back and forth multiple times on multiple markets, all without issue, but the second you try to remove those funds from their platform is when they hit you with account suspensions or investigations or other such crap. While everyone
should get their funds off centralized exchanges whenever they are not being actively traded, the
only way ensure the safety of your coins is to never let a centralized exchange hold them at all.
If you want to trade anything to do with foat money you will end up with CEXes following regulations. That's how real world works. If you want to be crypto anarchist, use dexes, don't use fiat money at all.
There are plenty of DEXs on which you can trade fiat for bitcoin and vice versa. Bisq is the best example.
That's a great list. I hope you update it regularly.

I'll try my best!
