I would add another dose of starter at the end of May. The only crabgrass preventer you can use now is Tupersan, and it won't be effective against other weeds that have yet to germinate except foxtail, and downy brohme. All the others like Dimension, Halts, Barricade will affect your new turf. Weed killers can't be used on your new turf until is has been mowed at least two times, and four would be much better.

I went ahead and spread granular weed killer only on 5/10. Now I am wondering if I should spread normal fertilizer, starter fertilizer, or weed and feed?

Is it too late for weed and feed? I'm getting a new wave of weeds and because I planted new grass in spring I have only applied starter fertilizer and also weed killer about 8 weeks ago.

Ouch. It's getting quite warm for some of that. I'm assuming that you have bluegrass or fescue - both of which - but especially fescue - if over-fertilized, will be more susceptible to brown patch.

If it were me I would spot treat with a liquid selective herbicide like Weed-B-Gone or something that is labeled for use on the weeds you want to kill. You should wait for the coolest day possible, and spray carefully, knowing that it could also kill the grass. Also, with warmer temperatures, spray can volatile and drift to non-target plants (i.e. trees, flowers, shrubs) very easily.

Don't apply WBG when it's too warm. I think the label says not to use it if daytime highs are above 85. But check the label because I may be wrong.