Am I scamed? FA exchange trading company is fraud? They are requesting taxes Are those thieves? https://www.faexchange.com/ 
I have created a balance of BTC with them and they now request to pay taxes in order to be able to withdraw my profit so I am worried about and wonder why they do no keep the taxes from my earnings?

Additionally to report that they do not allow any withdrawal until they receive the taxes however I have found out that they are included at "bad list" https://badbitcoin.org/thebadlist/index.htm
I do not have a bitcoin wallet; but FA exchange never advised me to open one.
Should I create one and request from them to transfer the bitcoins there? What about the taxes in this case, should be deducted?

Any kind of advice on how to continue further on to cash/ redeem my Bitcoin would be usable.
It is certainly not 'normal' for an exchange to demand 'taxes' in order to withdraw. If you have a positive balance on your account, and they are requesting that you send additional, new money to them, then I would say without a doubt this is a scam. Think about it: why would they not just deduct any 'taxes' as a fee from your total balance when you withdraw?

My advice would be to not send them any more money ($$, BTC, etc). I am sorry to say, but you may have to cut your losses, and just move on. If the amount lost was substantial you could try reporting the scam/theft to your local law enforcement, but there may be little they can do to help.

You can try making a wallet of your own to withdraw the BTC balance to, but I would guess they will not allow this withdrawal either. 

As an individual, you may be liable to pay taxes on your cryptocurrency trading, but this liability would be to your local tax authority.

Sorry for your losses :(