pre-em last for months depending on what you used and how much you applied. If you plan to seed don't use any. You really shouldn't need to seed bermuda. If it's getting adequate conditions it'll come back and fill in. It can't handle shade and needs a lot of nitrogen..... Same as the weeds. Figure out why it's not doing well and address the issue. Fertilize, mow, water, and give it time.

Q4 is a decent cover all bases herbicide for those weeds. There are plenty of other options.

Something like this. Or you can buy a hand sprayer if you need something smaller.