Are you supposed to eat the rind of Brie cheese?

It is edible, but there's definitely mold on the rind of brie. (Much like a lot of cheeses). Personally I don't like the taste; so I cut through the rind and eat the nice creamy part of brie. Most every cheese that smells (limburger cheese, etc), smells the way it does because of the rind.

I like it fine; on good cheeses it seems like that outer layer has a lot of interesting flavor. I love it when at things like industry conference buffets thrown by giant rich corporations the good (or great) brie rinds gets mostly left behind for me :-)

If you don't like the taste of it, don't eat it. I suggest adopting that policy as a general rule. You might consider using the rinds with other old cheese nubs from your fridge to make cheese spreads/dips (food-processored with some white wine, a little salt, maybe mustard, etc).

It's a personal preference. It's certainly edible, and it won't hurt you. I find the texture a little weird. Generally you can eat the rind of almost any cheese. However, make sure you're not mistaking a wax coating for rind.

You don't have to, but I think it adds to the texture and gives an interesting counterpoint to the cheese.

If you're doing baked brie in puff pastry, however, I'd recommend shaving it down so that its thinner...the extra layer gets a little weird, makes people struggle with it.