1. I have KBG PRG mix. I cut mine at .625 which is 5/8". I do not know that I would go much lower than that. I may try .500 but that is probably the lowest I would ever go. The lower you go the more often you have to mow which can be both a good and bad thing. .750 looks really nice and is really a good happy medium.
2. I think you are going to have a tough time over seeding the KBG. It probably can be done but the KBG takes so long to germinate and waiting for it to germinate while needing to mow will cause problems because you will constantly be disturbing the soil and the KBG seeds need to sit for a minute and be left alone. I would say to give it a shot in a test plot. I seeded the KBG and had it growing for about 2 years before I over seeded with the PRG.
3. Sand whenever the grass is growing very vigorously. That would be spring or fall. It takes some time to recover and grow through the sand. Do not go too heavy or it will not recover at all because the sand pretty much suffocates it from sunlight. You have to have blades showing through the sand to get some sun. I have areas in my lawn that never recovered from sanding
fall of 2017. These areas will recover in the spring with fert, time, and KBG. The good thing about PRG is that its cheap and easy to over seed and grows quickly.
4. Yes. Your going to have to get the thatch out if you want to go low
. Thin it out big time with verticutter/slice seeder or thatch machine. Get it good and thin and then throw some more PRG seed down. One down side of PRG is the it does not creep and fill in. Seed is fairly inexpensive so keep putting it down.
See some of my videos.
I recommend getting a heavy greens mower. They flatten out the lawn over time and it might be easier to find a mechanic to sharpen it for you and for less coin.
Bottom line is that your lawn will be as nice as you want it to be. It all depends on what you are willing put into it with your time and effort.