Is that true that we have to move all our coins to a bitcoin core wallet so that in case of a fork to Bitcoin ulimited we have our coins also there? I heard that it is not good to leave the BTC at exchanges because they won't deposit these BTU 1:1 to BTC. Anyone knows more?
Here is my opinion. To get your BTU you must move or keep your bitcoin on the direct wallet which means you're using the software wallet. BTU will be running on the different chain or in this time I will be believing about the forked chain from the original bitcoin itself. So, you must wait until the forked chain will be fully activated. And the bitcoin unlimited dev will make an announcement or a method for you to get your Bitcoin unlimited.
Afaik, the problem is that without replay protection (which apparently BTU refuses to add), you would end up transferring your BTU when ever your transfer your BTC (and vice versa if BTC doesn't have replay protection). This was apparently a problem during the ETH/ETC split wherein some people tried to sell one or the other, but ended selling both as the transaction got relayed to both forks.
You can't even be sure an malevolent actor won't send your transaction from one peer network to the other.
I actually haven't studied this technical detail, so I might have an incorrect understanding.