There is no minimum. Occasionally riders will put their pick up and drop off address as the same. That doesn't trigger any concerns that the trip is too short either. If it's not a share, the address can be changed.
Do Uber drivers get paid more for longer distances?
Consider San Francisco, where miles are worth $1.30 and minutes are worth $0.26. If you drive 20 minutes on the freeway, you'll earn 80% of roughly ((20 x $1.30) + (20 x $0.26) + ($2.20*) or around $26.70. If you drive 20 minutes in town, you'll earn well, much less because your miles are going to be reduced.