questions:

Let's say I bought some IOTA in bitfinex. Now I create an own wallet and transfer my IOTA to the wallet to not be dependent on future events that may occur on the centralized exchange.

Well, at IOTA I also choose a NODE-server in light mode. If I choose the server bitfinex offers (or any other), is it not the same as to store it directly on an centralized exchange?

What happens, if the server goes down for example or hacked? Aren't my funds lost as well?
Or are my funds copied to every other IOTA tangles?

If it's just on one tangle and the tangle dies due to hacks or deletion, than the funds are lost?