Depends on whether you will be able to find employment or not.
No, that part doesn't matter. As the parent of an EU national, she's got the right to stay in the EU.
is there a possibility that I can stay here without marriage?
Absolutely. It is critical that the child obtains Polish citizenship - as a result of that, you can move to a more friendly country for Indians (the UK) and get on with your life there. The English legal system will have no problems enforcing a child support order on him, too.