Yes and yes. They do have a lot of recoil, but anyone who can shoot a 30-06 should have no problem with the 45-70. The round is as deadly as any, given its relatively short range. Mountain Sheep may be the only American game animal that the 47-70 would be inappropriate for, and that's because you can never get close to them.
That being said, a single shot rifle may not be the right piece for dangerous game like bears and cats. I love the 45-70 and the whole historical firearms thing, but would recommend a lever action rifle, for speed and ease of follow up shot(s).