Yes, they will charge fees for both trading to another currency (crypto or fiat) and withdrawing regardless of the destination.
Thank you for your answer.
I have a small selection of altcoins/tokens in my portfolio on different exchanges but I want to store all of them in one place from what i have read I shouldn't keep them on exchanges as they are not regulated and not 100%safe. What would you advice?
Depending on the altcoins you're holding, you could look into a multi-coin wallet like
Exodus which supports over a dozen altcoins. If you still have altcoins that aren't supported by them, you could either use the wallet they recommend you to use, or look into something like
Coinomi which supports over 64+ (!) altcoins.
Jaxx.io might also be an option, but i believe that they had security issues in the past.