F9 is not believed to have any information from ground sources during descent, based on FCC filings. The altitude of the barge only changes by a meter or so in decent seas, and the legs can withstand a drop of several meters, so probably they target sea level +N, where N is the maximum expected height of the deck.
The ship can hold position to within less than a meter. It's easier to just plan the position beforehand than try to have the rocket receive the ship's position in realtime somehow.
It's interesting to consider how much more difficult this stuff would be without the GPS satellites already in space.
It has very good inertial guidance as well. The GPS is probably the best available; considering they launch GPS satellites, I'd expect they aren't restricted. However, civilian GPS use isn't really much different anymore; intentional degradation was turned off in 2000, though certain dynamic limits still apply on the receiver side.
I don't know if they care too much about redundancy. The landing is still very much optional, after all. They have no redundancy in case of engine failure for this phase, which is probably much more likely. GPS is kind of inherently redundant anyway, as long as you have multiple receivers. You need four satellites for positioning, but way more than that are visible at any given time.
