No because the highest you can get without going over is 99. If one cat catches one mouse in one minute and there are 100 minutes to catch 100 mice then you only need one cat. 3 cats would catch 102 mice per 100 minutes.
No, 3 cats catch 3 mice in 3 minutes, not 1 cat catches 1 mouse in 1 minute. Who's to say they aren't working together? AND by your logic, you would say that the three cats are going 1 at a time, but in fact each cat is working on one mouse each, and they take three minutes to catch one mouse a piece. So if that were the case, then it's 4 cats, but I'm assuming they are working together.
So it's either 3 or 4. (but I think three is the answer to the riddle, not a real life thing)