You'll be OK. I do this all the time. Put down seed and for one reason or another it doesn't germinate in a few spots, so I put down more seed in those areas. You'll have to water a week or so more than usual, but not really a big deal.

From what I understand about 'starter' fertilizer it has a higher degree of phosphurus---the middle number---and lower than usual amount of nitrogen...the first number so to prevent growth of the resulting seedlings until they gain some strength. I don't believe what fertilizer you used...20/10/10....is a type markeded as 'starter' type. I've never used a type such as this, haven't had to 'fix' a lawn but I have regularly overseeded my lawn in both spring and fall....and overlayered a topping of compost as well. I think there is a question of whether cutting a lawn short in the fall does any good. Yet many do and swear by it. In New Jersey there is still plenty of time to overseed a damaged lawn and bring a new lawn into existence.

If it was me, I would not fertilize now if you did a full application of actual nitrogen when you seeded (1lb per 1,000 sq. ft.). However, it may give the grass an extra boost, and it probably wouldn't hurt anything if you wanted to. Half rate would make sense, though. Also, I think a lot on here would discourage the use of winter fertilizer. A soil test would tell you for sure what you need, but if you don't have that, a "regular" fertilizer, would probably be just great. What are the numbers on the winterizer bag?

Green kyllinga is not a grass, it is a sedge. Traditional grass killers do not work on sedges, so you have to have a sedge killer. Hopefully the Dismiss label will tell you what it is. If your lawn is overrun with it, it is more likely to be nutgrass or nutsedge. Kyllinga is a slow moving plant while nutgrass is a very fast moving plant. The only way to tell them apart is to look at the seed heads (on Google Image Search). Assuming it is nutgrass, did you get a lot of rain this summer or did you water the lawn more than one time per week? Because nutgrass is a swamp type grass that can be slowed way down by watering every week or two (or 3 or 4). Kyllinga is not a swamp grass and is not intimated at all by dry soil, but again, it does not spread nearly as fast as nutgrass. So if this is nutgrass I would be inclined to wipe it out this season. If it is slower moving kyllinga, then wait until spring. There's no need to aerate if you're overseeding (or for any other reason in my opinion). Why do you do that? I know a lot of people do it and you can find recommendations to aerate all over the Internet, but I don't think it's necessary (ever). Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.