Sorry. Only if the complete position is repeated 3 times with the same side to move is it a claimable draw. The situation you describe could also come under the heading of a perpetual check if the helpless king you described is being endlessly checked and has no escape. A stalemate is where one side has no legal move, but is not in check.

Opinions vary on this one, but let me give you a few helpful ideas. I am going to assume that you are playing in events where you may not know who you will be playing.

1) Possibly the most helpful thing you can do is to deeply analyze your losses. Finding out why you lose games is a critical factor in discovering the areas you need to strengthen about your game. Find a more advanced player to help you or use the various chess engines (crafty, fritz, etc) to assist you in your analysis. This should be done after every tournament so that every time you enter a new tournament you have a better handle on your own strengths and weaknesses.

2) Go over all the main lines of your opening repertoire before every tournament....even if you know them "backward and forward". Reviewing this information is all important and helps prevent opening mistakes like transposition of moves. Even the great Kasparov made this mistake in his final game against Deep Blue. If it can happen to him, it can happen to you. Know your openings.

3) While I'm on the subject, DON'T try to learn a new opening the night before a tournament. The time for this is in training games or offhand standard games, NOT your first round of an important OTB tournament.

4) The week before the tournament, play some training games against a better opponent. One trick I've learned is to play these training sessions at a time control 15 minutes or so less than the time control of the tourney you are going to enter. That way, if you have some unexpected problems over the board, you have an "extra" 15 minutes more than you are used to in your training games.

5) I've mentioned this before, but can't emphasize it enough: go over some "white-to-play-and-win" type books. Constantly reviewing middlegame situations keeps you tactically alert. Your brain stores this knowledge. Boris Spassky was once asked how he decided on his moves and his reply was that he didn't really know, the move just "came" to him. This intuitive-type approach is a result of reviewing thousands of positions.

6) One factor too is the type of tourney you are entering. Players tend to need to play more aggressively and use double-edged lines to win Swiss System tournaments. On the other hand, if you are playing a match or a round robin tournament, then "not losing" is almost as important as winning. Check out crosstables of major events and you will be surprised at the small point margin that separates first and last places in the big Round Robins.

I hope this helps you. Good luck in your next event!!