Bob to answer more thoroughly,
1. Will a new queen sufficiently mate in late summer dearth? Only if sufficient drones are present. why not wait a month, or until you have drones.
2. In the next 2 and 1/2 months, through dearth and fall flow, will she lay up a 5 frame nuc of winter bees?
Answer: If you can keep them from getting robbed out, If she mates, maybe. Just give it the old Irish try, then you will know what to expect.
3. Skipping this one.
4. Can late season splits succeed?Answer: Yes, I do it every year. Start 2nd week of AUG. or when they start making Drones. But I only run about 70 percent on mating and about 30 percent of those dont winter over. So 40 percent is what I have from them. Drones are scarce in the summer, better in fall after the minor flow starts. If you start in the summer you need to keep up on the robbing issue. After the fall flow not so much.You could get mated queens But they have probably been banked.
I would say just do it, and figure it out for your area, and good luck, let me know how it goes.