If your prostate was operated on to decrease its size, is it possible to father a child afterwards?

Yes. If you don't ejaculate after a turp, you are still making ejaculate- it is just going "retrograde" into your bladder. A fertility expert can help extract the sperm so you can use it.
Usually, yes. Although erectile dysfunction is a possible side effect of the surgery, sperm can still be obtained via another method to fertilize your partner's egg.