Exchanges establish their own fees. The fees are different not only between exchanges but sometimes between different trading pairs on the same exchange. Use a free service like Switchain to compare rates between a few different exchanges for each individual transaction.
There are custodial and non-custodial exchanges. Put simply, the first ones hold onto your assets that you leave with them which is what makes it vulnerable. Once it's hacked there's nothing you can do but watch. Non-custodial ones only hold your assets for the time necessary to complete the exchange.
Hope this helped.
It’s best to not have your coins in only one exchange so that you don’t lose them at once in case such a thing happens and the exchange is attacked by hackers. So have different exchanges and only have the coins you want to trade with on exchange and once you’re done with it you should move it straight to your wallet, cause there it will be much safe than on the exchange.
As a result of some of the security lapses that has happened in the past and how not to be a victim again in the future, I totally agree with this. No matter how reputable an exchange is right now, they cannot be trusted, simply because you do not have a full access to your funds and that way, you will always need to be very careful.
At least, trading on two or three different exchanges kind of spread the risk and it is a good thing that with the likes of application like tab trader, where you can have all your trades from different exchanges done on one app, it makes things a lot easy.