1. Look up "premove"
2. It looks like you ran out of time in the game where you had two pawns and the result was a draw. If you run out of time, you can't win. Normally you would lose, but if your opponent can't checkmate you (as in your game) you get a draw.
The games here are straight up.
Well, in the last example apparently your flag has fallen, so you would lose, but since your opponent had no material except his king, you got a draw.
I also suggest that you read a FAQ on lag on live chess.
If you still think something is wrong, maybe you should contact support.
I have played several games in the last week where the opponent has been able to add more seconds to the end of the game. The game clock actually hits 0 and then there is a pause and more seconds are added. This happen three times in one game this week. Today at noon central i was playing a game and I obviously had my opponent beaten when time runs out on him and all of a sudden I get "Draw" thrown out. There is no way it was a draw. I had 2 pawns moving toward the back rank to convert to queens.
Please clue me in on what is happening. I have left other chess sites because players were using programs to win games. If the games are not straight up then what is the point?
Thanks