It's free software (https://github.com/lichess-org), and you only need web browser to play [1]. Even Magnus Carlsen and many other top Grandmasters play there.
As for cheating, all games are checked for computer play, so even if you can occasionally lose a game or two from a cheater, he will be caught, and you will get back your rating points (if you care).
I highly recommend Chess Tempo for tactics training. A large database of problems drawn from grandmaster games, insightful user commentary per problem, and a full classification of each problem by the type of tactic e.g. attraction.