lawn fixing for spring (flowers, crabgrass, insect, weeds)

[ovi8]

I'm in NY and this was a newly sodded lawn from 2 years ago. Last year I made the mistake of not putting down crabgrass control (didn't have the problem the year before and it was new) and had a ton of crabgrass taking over my lawn. I pulled a lot out by hand and apparently got some kind of summer patch disease that browned a huge section of the lawn. I re-seeded (kentucky bluegrass seed and peat moss) late this past fall and got the brown to come back with a little green again before and throughout winter. Also put down winterizer.

Right now in early spring, it's starting to show some new kinds of weeds - maybe it's the early stages of dandelions, but there appear to be 2 types. One has the white flowers and the other only has thick green roots so far.

Since the green grass is still not too plentiful, I was going to rake/clean and then overseed some more. With the new weeds in question - I'm not so sure if that's what I should do first?

The annual regimen I was told goes like this:
- Fungicide mid april if necessary
- Crabgrass control with Feed late Apr
- Weed & Feed. Late May
- Insect Control with Feed late June/July
- Turf Builder early Sept
- Winterizer (no weed killer) Oct-Nov

Or maybe it's still too early to do anything? It's still relatively cold at 50F these days. Just don't want to let the weeds take control again.