Yes. In order to fight the final boss of each instance on heroic in a given week, the rest of the instance must be dead on heroic.
I'm guessing you guys are debating it for achievement reasons (gotta get that glory mount), so yeah. You'll have to skip a week of loot for those glory metas that you have to do on normal.
Depends. In BoT, you only had to kill H Cho'gall to access Sinestra. In FL, you had to go 6/7 HM to get to Ragnaros. I don't think we'll know until 5.2 comes out.