Are there sites where i can play games and earn 0.001 btc per day?
If you are looking for free faucet games try this one
https://bitcointalk.org/index.php?topic=1317322.0 it is possible to win more than 0.001
BTC.
So there are no game sites where i can earn 0.001 btc by playing 2 hour nonstop?
Not really, you can win that in casino games. Hm, almost every bitcoin casino has faucet so you can try your luck and maybe win that amount in 2 hours.