I wouldn't fertilize yet. If you do, just use something like 21-0-0, but apply it at half the normal rate.

The soil around here has plenty of P and K naturally, so there's no need to use a starter fertilizer.

It's still fairly cool, which is fortunate for you. Normally, by now, it would be getting hot, so you've got some extra breathing room. But you still got a pretty late start, so you'll probably need to water quite a bit this summer (I hope you've got secondary water).

Since the grass is only coming up in some of the aeration holes, I'd continue with the 3x per day watering. With the cool, relatively damp weather we've been having, 5 minutes at a time will still work.

I'd probably continue watering 3x a day for 5 minutes for the next couple of weeks. After that, cut back to watering 2x a day for 10 minutes for two weeks. After that, you'll probably want to go with 1x a day for 15 minutes. Since it will be right in the hot dry part of the summer by then, you'll probably need to water every day until late August. Then you can start to cut back to every other day until the rains and snows start.

Next spring, hold off on watering until the lawn starts showing signs of stress, then water deeply. The goal is to water just once a week, but with our low humidity and high heat, you'll probably find that you need to water at least twice a week. But watering daily after this year is actually counter-productive (although many around here do that). If you're in one of the sandy areas, you may need to water 3x a week. But even in the sandy areas, daily watering can lead to problems. I once read that the most common lawn problems in the Salt Lake valley are all due to too much water (kind of ironic considering it's a desert).

I would not seed next spring at all. If your fall seeding doesn't completely fail, a spring seeding won't be needed. If it does fail, I'd put seed down just before the first good snowfall. The snow melt and freeze/thaw cycles will bring the seeds into contact with the soil and the seeds will germinate early in the spring with the natural moisture from snow melt and any rains we get. Areas of teh lawn that warm up sooner will germinate faster than areas that are slower to warm and you'll get a jump of several weeks on a traditional spring seeding.

I only water 3 times a year, but I have clay soil and mostly native grasses, so the roots extend several feet into the soil and the grass is well adapted to very little water.

If you water deeply, you should be able to keep a Kentucky bluegrass lawn green with no more than twice weekly watering. You'll only get by with 1-2 times a month if you have a lawn with native or naturalized non=native (like crested wheatgrass) grasses.