Is it possible to take a purchased figure change it to being overweight and then morph it to being slim?

Yes. Poser comes with a female figure that has an "endomorph" (fat) morph. IMHO, it's not very good, though. Still, you might want to see if Jessi, the Poser 6 female, is good enough before you buy anything else.

Mostly likely, you will want DAZ3d.com's Victoria 3 figure. The base is free, and you can add your own morphs if you're skilled in a modelling program. You can also buy her morph pack, which is very reasonably priced. It contains pretty good morphs for making her look chunky.

You can use BVH files with Poser, and they should work at the same time as the morphs.

Dunno about broadcast video. I've never had occasion to do that. Someone else here probably knows, though.