Yes. It happened to me once. In my case, I withdrew from my gambling account to my exchange account and I got asked by support to provide some more details. So yes, almost all top exchanges prohibit depositing/withdrawing from/to gambling platforms to their own platforms.

Ya. Just do it like this:

Gambling platform <> Own wallet <> Exchange account.

These exchanges don't just want to be tied directly to gambling platforms. Once you avoid that, you're good to go.