How long can I leave the eggs in the nest to try to get my hen broody before I take them and put them in an incubator
Don't leave eggs in the nest - put ping pong balls, golf balls, plastic easter eggs or some other roundish items in there. The chicken won't know the difference and will happily sit on them to hatch if they are broody. Eggs left in the nest are an invitation to bugs and breakage - two things you don't want. Once your girl goes broody - that is stays on the nest for 3 nights rather than return to the roost & stops laying eggs - then you can move a batch of eggs under her to hatch.
I've left eggs on my kitchen countertop for a week and then moved them under my girl to hatch. She did just fine hatching 4 out of 5 eggs.