can this be resolved by itself if I wait?
Given the very low transaction fee that prevents your transactions from being confirmed, it is not realistic to expect the situation to resolve itself. Mempool is almost 200 MB, and the number of unconfirmed transactions is mostly around 100 000 - so you have to take some other steps to get what you paid for. I suggest contacting that exchange via chat or ticket support, and if they ignore you the only way to get things started is to push them through social media, it usually works.
I can’t remember ever hearing of something like this - Coingate was obviously quite messed up somewhere.