Risks in joining websites that offers bitcoins for trade I have joined a website in our country that offers buy and sell of bitcoins,the only one that offers our currency. When joining websites like this, what should be the right way in terms of getting or obtaining the bitcoin address?

Upon registration, you are given your on address by them. You can buy/sell bitcoin on their website. For me that sounds fair, nothing strange. But then, last week, I bought an amount of bitcoins from them and I can see it when I logged in to their website. But checking https://blockchain.info/address/&lt;my bitcoin address&gt; shows no bitcoin balance.

I have checked a friend of mine's account which has transaction outside the website and can see it receiving bitcoins but the final balance is zero. But looking at their website, the balance is there. If I bought that bitcoin, why is it not in my wallet?

In addition, if you transfer to a bitcoin address outside their website, the fee is likely more than twice than using others like coinbase. I think this is for keeping you inside their website. Like for example I tried transferring 10 USD, and the fee is 15 USD. I have to cut out 25 USD on my address just for that. Crazy.

Are these things which I should be worried about?
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