Depending on where the Flatheads are in your waters, you are a bit on the light side with your line. Flatheads love cover and you had best get them out of there on the first run or they will snag you up good.
As for your other questions:
1. I don't think Flatheads are very discriminating fish. You really don't need a leader at all. They don't scare off by seeing line.
2. See my opening statement.
3. I can't get a Uni to stay put in PowerPro. I use a Palomar.
4. Carolina rigs are OK, but if you are dropping baits into cover, a long leader will drive you nuts with a lively bream on the end of it. The best thing I have found is to use a basic offshore Grouper setup called a knocker rig. Tie it up like a Carolina with the line through the weight (about 6 to 8 ounces), a small plastic bead on the line next, then the hook. The weight sits directly on the hook.
5. See above.
Tom
PS: Flatheads in Florida are a introduced exotic and considered a trash fish. No limits, and it is against the law to return one alive to the water. If you catch one, kill it even if you don't intend keeping it to eat (which would be a shame as they are great table fare).