1. No, Heat of Battle does not increase PvP experience.
2. It will take you quite a few battles to reach 38. At least a few hundred. The more you play obviously, the quicker you will get there. But realistically you are looking at several weeks.
3. VIT accessories are not a bad idea. The more HP you have, obviously the better your chances of survival. But again, gear syncing down to ilvl 80 is the biggest limiting factor here.
4.-6. Materia has such little effect in PvP (FL) that I have never really worried about it. Concentrate on streamlining your rotations and teamwork abilities. These will help you contribute much more than any materia.
8. Play and enjoy. A lot of inexperienced PvPers will be with you and you will lose a lot. Dont get frustrated and keep working at getting better. Healers are the PRIMARY targets in Frontlines and therefore a lot of Healers get frustrated and want to play other jobs.