With the tree I removed I just used the chain saw to cut it flush with the ground, but I'm guessing you could probably just rent the tool to grind down the stump.
You could do that. It can be difficult using a chainsaw too close to the ground as you start to get roots and such that grow more horizontal than the trunk, variations in the dirt that might make it difficult to get around one side, &c. You could definitely get it down to 6-8" above dirt without too much trouble though. The thing about the trunks is you want to cut it into pieces maybe a foot long each, at most. I don't think anyone can dispose of a giant log. :)