3. I just read you should collect the clippings so the mulched grass doesn't cover the soil...that's a lot of work for me, is the core aeration enough to take care of that issue?

using a core aerator after a rain may leave 2-3" holes in your lawn. You don't want the seed that deep.
I would consider a dethacher or a power seeder

I agree with dmoore66. Just because every professional overseeds this way, and not every one does, does not make it right. Mother Nature seeds by running dense herds of ruminants (bison, zebra, antelope, etc.) through the plains where they knock the seed off the grass and stomp on it. AFTER THEY LEAVE the area, then come the dung beetles which dig holes in the ground. But the seed goes on top and should be stomped down to replicate the way Nature does it.

Having said that, many professionals who do aerate get good results. Personally I think the aeration done by professionals is more motivated by their need to make boat payments all winter than it is by the need to improve the seeding process.

I would cut the lawn as low as the mower goes.

I would use a dethatcher or a slit seeder.
Better do it soon or wait until next year.

The 1/3 rule just keeps you from stunting the grass. If you chop too much off, it can really slow growth down while the grass recovers. Normally, that is a bad thing and will leave you with a sickly and patchy looking lawn. When overseeding though, it is ok if the old grass is stunted for a couple of weeks while the new seed gets going.

I also agree with dsledge. I have aerated most every year that I have seeded. The couple of years that I did not, were miserable failures due to heavy rains that completely washed the seed away with a couple of days. I had to completely reseed in those years - a huge PITA not to mention $$$.
I just put my seed down yesterday, and due to both time constraints and a tight budget this year, decided to forgo the aeration as we are not due for any rain this week, at all. I plan to water appropriately with my sprinklers, to get the seed set properly. I may even walk the yard in the bare spots (I have several - our summer was just brutal). If you have the time and money to aerate, I highly recommend it. It has always worked best for me. I am keeping my fingers crossed this year.

I don't think it was ever mentioned, what type of grass are you growing/seeding? If it's something like tall fescue, then 1.5-2" would be too short, I would think it would severely stunt/hurt the growth. I would mow it to 2.5" max.

And if you have really heaving clay soil, then you definitely want to aerate. Otherwise it's going to be so compacted, that the old grass roots are going to stop spreading and kill the grass; and the new seed won't be able to get started if the soil is rock hard.

I agree with Bill: "When overseeding though, it is ok if the old grass is stunted for a couple of weeks while the new seed gets going."

In fact, it probably helps the new seed get a needed leg up on the established grass.

I've tried just about every way of seeding. The slit seeder is the cadillac option. Then aerating, then just broadcasting. I recommend a yard roller, per Dchall's press it in statement, regardless of how the seed is put out. A yard roller is cheap, easy and fast.

I aerate and then over seed. It came out great the first time I did it a few years ago. I will be doing it again this week.