I would suggest alot of back bends, to stretch your back. Keep your feet together, and legs straight, puch until your head is over your hands. This will help the flexibility in your back and help with your kick over.
As for handstands practice up against a wall, shrug your shoulders while in your handstands. Also when you're at practice doing handstands when you go to kick from your lunge reach out as far as you can, this will keep you from putting so much power that you fall over. Keep your muscles tight!
Kartwheel- Its like a dance move find a line you can work on. Lung. First hand on the floor is beat 1, second hand beat 2, first foot beat 3, second foot is beat 4. It will help if you have a metronome.
Round Off- I don't have any drills for this one... Just make sure you're getting your left hand (Right hand if you use your left leg) around to the other side of your right.
I don't remember doing handstand dismounts. I started team when I was 7, and I was doing round off dismounts.