You best bet is get a genarator and be done with it, and you could also set up to run your tv and a few lights. A hand pump is a bad Idea it would only fill a pot before you would have to pump it up again.
I think you have a broken sewer line and its taken in rain water just like the ground water system would. I strongley recomend you have a camra ran down main sewer line to find the problem.
Theres a rubber gasket between the bottom drain piece and the shower floor. Remove and replace it, that rubber ring IS you main seal. It may be a little snug but it should slip out.