so I have 2 questions(1,2,3) :-)

1. Yes. Just let them die where they are, no need to remove them.

2. It will be ok. For next year you will use pre-emergent and prevent them from coming back from seed.

3. If you want to fertilize, use a fertilizer not weed and feed. If you have the weed and feed on hand and want to get rid of it, you can apply it no problem. Keep in mind the "weed" part only works if the grass is wet so the granules can stick to it. If you just apply it to a dry lawn, the herbicide is pretty much just wasted.

Sure. Relax. If you want to kill weeds, spot spray them with a liquid as you apparently did. Do that in mid April. If you want to fertilize, do that with a fertilizer, but don't jump the gun on that. If you live anywhere but the hottest part of the deep south, then wait until late May to fertilize. Note that the time to kill weeds and the time to fertilize are many weeks apart. That's the reason why weed n feed products don't work.

Just let the dead weeds decompose. Many have already seeded and will come back. Next time you see them, get after them with the spot spray right away. You will get rid of most of them the first time, but it might take 2 or 3 more apps of herbicide to really do them in.

If you have thin grass, you will have more weeds come in. In the north you can reseed in the late summer to early fall. That is the best time of year to reseed in the north.