Two different animals. Stalemate is when one side is on the move and not in check, but has no legal moves and the game is automaticlly a draw. Three position repetition is when the same position has come up 3 times (not only just in a row) and the player on the move can claim a draw, but is not required to do so.
When you sign in to RHP, there will be a section "Available Tournaments" (I currently have 14 I could play in) if any are available for you based on your sub status and rating. Non-sub tourneys are rare.