I have a long hallway that I would like to redo with 3/4" hardwood floor & base molding. At the end of the hallway a staircase leads down. I am planning on starting with a 3/4" stairnose and then working my way back down the hallway. First question: should the hardwood planks be installed parallel to or perpendicular to the axis of the hallway?

Also, I need some advice on the stairnose. Don't I need to leave an expansion gap on the sides of the stairnose where it meets the walls of the hallway? If so, how do I cover the gap, it seems like I would need some kind of weird curved base molding to wrap around the stairnose. If I'm supposed to install the stairnose flush with the side walls (without molding), how do I transition from the base molding running along the hallway?

Thanks for any suggestions.

The stair nose is cut tight to the sides. Wood does not continue to grow with the grain. It is cut, it's dead. Now in the width, is a different topic about wood vessels.

The hardwood planks should be installed across the joists under the plywood.
Hopefully and usually this is the long way of the hall.
To transition the base, there are a number of ways. You can just miter the squre cut back and paint the end. You can miter the square cut towards the wall and install a small mitered piece to the wall. This is a return. Theres more but thats probably what you want.