Does the 3 train stop at Penn Station?

Yes, the 3 train stops at Penn Station. All trains on the 1-2-3 line (the red line) and the A-C-E line (the blue line) stop at Penn Station.

However, the 3 does NOT stop at Penn Station from 11:30 PM to 6 AM. During those times, the line ends at 42nd Street-Times Square.