This is tricky. For one, I like the way you look from the kitchen down to the gallery wall - makes it look nice and long, but I also like the way the wood would line up with the stair treads if you ever decided to go hardwood with those instead of carpet. Do you use the room with the gallery wall more than the one with the TV?

Wow, very good point about the stairs. In a year or so we will be doing the stairs so it will look better if the floor will line up. And yes, we definitely use the room with gallery more than the TV room.

My inclination is to establish the pattern at the entry with the plank pattern going from longest (or widest) wall to wall distance. In the project pictured the longest dimension of plank ran from front entry down hall. The pattern continues through the adjacent living room and dining room.

If there's a subfloor installed, I don't think it matters. I don't know that many hardwood manufacturers recommend installation directly onto joists anymore.

I'd do it lengthwise towards the back of the house.

@kmcarney I have no idea :)

Solid hardwood (as opposed to engineered or any of the faux woods -laminate or LVP) should be installed perpendicular to the floor joist.