Help me with a plan of attack

Hi all. I am a relatively new homeowner just looking to get my lawn in slightly above average shape. My wife and I moved into our house in fall of 2016 and unfortunately, the 6,000 square foot lawn is not in great shape. We have clay soil. Half of the lawn is decent and certainly presentable, but the other 3,000 square feet is probably 40% bare or thin, with a ton of weeds.

Last fall, I paid a service to core aerate and power seed the lawn. I watered diligently, but results were not great. In a few spots where I added topsoil (such as 30 square feet where a tree used to be), the grass grew in decently, but not in the rest of the lawn.

The company came back ten days ago to power seed the entire lawn again, but I'm not seeing much come up this time either. I also know that spring seedings are hard to maintain throughout the summer, so I'm now attempting to formulate a plan of attack for fall and I would like to do it all myself.

In general, here are my questions:

1. Can I use weed killer such as Weed B Gon on the lawn in the summer and still seed in the fall? Say around 8 weeks apart. I believe the answer is yes but want to confirm.

2. I believe that a big part of the problem may be my soil. What is the most reliable soil test? I'd like to get the soil in good order so that whatever hard work I do and money I spend in the fall is not for nothing. Would I amend the soil in the late summer or fall and then aerate and seed immediately after?

3. The lawn has some thatch, but the biggest problem seems to be the compacted soil. Does aerating accomplish the same thing as dethatching, or would it be recommended to do both?

4. Once I have the soil amended, what is the best plan of attack? Aerate and overseed with a spreader? Or do I need to slit seed? How about timing and order? Aerate in early September, then two weeks later seed? Or do them at the same time?

5. How much water is recommended? I have been watering the lawn 15 minutes, twice a day in each spot and it seems to be saturated, with puddles even forming in a few spots immediately after watering. Is this doing harm to the lawn?

Thank you for any and all advice.