Risks in joining websites that offers bitcoins for trade
It is likely that the address you were given upon joining is a deposit address, that you would send bitcoins to when you want to sell them. When buying bitcoins, the site will hold them for you until you withdraw them to an address you provide. Usually that would be a separate wallet, e.g. a program on your computer, hardware wallet like TREZOR, or a wallet website like the one offered on blockchain.info. Until you withdraw the bitcoins from the website, they hold them for you, which means there is more risk of losing the coins if the site gets hacked, goes rogue or goes bankrupt. There is a saying in the bitcoin community, that if you do not have the private keys then you do not own the coins. So the safest route for you is to get your own wallet and withdraw the coins there, and then make a backup of your private keys for that wallet. 

And yes sites like that can set their own fee, some might be ridiculously high unfortunately, but there is not a lot you can do if that is what they ask