MTG Salvation

If I Exhume Griselbrand then use his ability to draw 7 cards and my opponent in response Swords to Plowshares him, do I still get the 7 cards?

Yes

Yes, once activated abilities exist independent of their source. To stop you from drawing cards he would have to counter the ability on the stack.

Yes.

Exhume resolves, and puts Griselbrand into play

You get priority. You choose to put Griselbrand's ability on the stack. Then you pass priority to your opponent. Now is the first time your opponent gets to do something after Exhume resolves. They play STP on Griselbrand and pass priority back to you. You pass, and STP resolves, exiling Griselbrand and you gain life. You get priority again (and Griselbrand's ability is still on the stack). You pass, your opponent gets priority and passes, and then Griselbrand's ability resolves and you draw 7 cards.

Removing the source of a an ability doesn't stop the ability from resolving. It's like if Fred throws a grendade at Tom, and then Tom shoots Fred, it doesn't stop the grenade from being thrown.

Exellent! Thank you!