Does Betfury let you withdraw coins without prior deposits? Or the coins are only free to "play"?
Yes, you don't need to deposit anything. I didn't deposit anything and already received multiple payments.
I thought that you had to have 10BFG at least for staking?
Correct. You need 10 BFG tokens to receive your rewards, but if you have less than 10 tokens, the rewards are already calculated but you can't withdraw them.