You may or may not be insane but 2-1/2 weeks isn't enough. I don't know any women that can do 50 push-ups. Even those who are training regularly. I know that some can but that is a tall order, especially in that short a time frame. As for the sit-ups, I did marshall arts for over 3 years and they always had us doing these super fast sit-ups and I could never understand it. You lose so much of the mind muscle connection doing them so rapidly. Plus I'm a bit more muscled up than a lot of people and I simply couldn't move my upper torso up and down that quickly. To get 50 you need to move pretty fast!
As to training to improve your numbers, do as many push-ups as you possibly can until you fail, rest till you catch your wind and repeat. Skip a day or two and do it again. Follow that until a few days out from the test. Add a set or two to failure as you go along and adapt. Lay off from other intense type training. You want to put all your energy into the exercises you will be tested on. Definitely allow a few days before the test to fully recover so that you are at your strongest going in. Good luck!!