Can you post a picture of your crabgrass? Because all the crab grass died last fall and should have disappeared by now. You might have a different weed, so to help you with that we'd need to see it. Best pictures are taken on a cloudy day or in the shade. Best identification pictures would have a seed head on the grass plant.

Why do you want to aerate? Is your soil hard? When it rains is it still hard?

You can use starter fertilizer, but I would wait until you have roots from the new grass before fertilizing. When you fertilize in the early spring, you will have to be out mowing several times per week to keep it under control. Spring grass usually grows very fast without fertilizer, so when you fertilize, with chemicals, it just goes that much faster. So I'd wait until you are mowing the new grass at a fairly high setting. That might be late April or even late May the way this spring is going.