1. Would there be any hope of finding a teaching job between December and January? What date does the second first semester end and the second semester begin?
It isn't the best time at all, but a lot of the work in Poland (especially Warsaw) is in-company so doesn't work on the semester season. It's also a time when teachers leave mid-contract. One problem might be Feria (a 2 week holiday in late January). Though it is possible to pick up work at that time. The new year is often a good time to pick up private lessons.
3. Is it acceptable to apply for jobs before I have finished taking the CELTA course?
During your CELTA is a good time.
Have you checked out the ESL Cafe Poland section? The search function there is a mine of information, especially about work permits for US citizens.