1. I suggest you hold off on the lime. You can put it down this Winter or next Spring after the new lawn is established.
2. There isn't going to be much seed in the raked up weeds-most of the seeds will already be on/in the soil, but rather than topdress with yard debree, consider spreading 1/4" or less of peat moss. It will hold more moisture in the soil and help hold the seed in place.
3.In my experience, you should allow the RU a week to kill the plant before you scalp.
4. That's going to be a lot of tamping if you are planting more than 100 sq ft. If you topdress with peat moss or another clean small particled material, rolling/tamping is not critical.

I checked out peat moss and I don't think I'm going to use it. The bales are too heavy for me, I would need lots of them, and they apparently make the soil more acid, which is the opposite of what I need to do to the PH. The stems of the dead weeds I'm killing should help to keep the seeds in place. Why would it not be a good idea to use the grown up dead weeds which have gone through the lawn mower as a topdressing? If weed seeds aren't the problem, what is? I also looked at some pellets like Pennmulch and though it looks like it would be very good to help retain moisture, it's expensive for the whole backyard. I'm home so I can do the light watering throughout the day.

One other thing I'm doing in preparation is working on a patch of hard soil where nothing grows (about 9 sq. ft.). I mixed some shampoo with water in the sprayer, sprayed the area, then watered it. I put some dead grass (from the front yard that I've been raking to prepare for over seeding) on top and watered it some more till everything was soggy. I'm hoping to soften up that soil in the next couple of weeks before I plant seed.

Dead organic material from the mower is fine to use as a cover for grass seed. Compost will also help, short and long term.

Thanks for the replies. I've decided to rent a roller. Should I roll the front yard too where I'm just overseeding? I'm going to have to do something with the dead material, so if it's not a problem to use it over the grass seeds, I'd like to do that. Otherwise I will have a mountain of dead weeds (the crabgrass was very thick) to stuff into supercans or pile up in the alley. I contacted Solu-Cal about when to put down the lime and got a reply to put it down with the fertilizer and seed. Solu-Lime is the same stuff as Solu-Cal, just Southern States' name for it.