Now I don't comment any game in progress. This is only information about rules, and how they are applied here at RHP:
Yes, there is a 50-move rule. If no pawn has moved, if no pieces have been taken, if a castling has not been done within 50 moves, there is a ground for 'claim a draw'. This draw is accepted automatically by the system, no involvement by your opponent.
There is also a position repetition rule. If a certain same position repeats itself 3 times there is also ground for 'claim a draw' as described above. Note that these three positions don't need to be in a row, they can be many moves in between.
None of these moves is done automatically, you have to 'claim draw'. If the draw is correct, then you get it without further qeustions by the system nor your opponent.