There are several things that must be considered. I like to use the concept of MOST amount of flooring that follows the general rule. If you have a single room (lets say 10' x 10' = 100sf) and then the REST of the space is much, much larger (say 600sf), you would want to try to keep the MAJORITY of the flooring (600sf) sticking to the rule of "longest length = long run of the room". The other question with hardwood becomes wooden subfloors. Sigh. Wooden subfloors over joists change the equation. Hardwood floors must be run perpendicular to the joists - no matter how big/small the rooms are. So...without knowing your set-up, without knowing your subfloor, without knowing the direction of sunlight, without knowing very much of anything about your situation...the majority of the home should follow the rule of thumb. Unless other factors contribute to changing this. Which I can't tell because there isn't enough information. And just for fun...diagonal is always an option = 15% waste and a more expensive labour bill.

Is your house on a slab or on joists?

IMO rethink the tile it is already a dated look and IMO never was a good choice. As for how to lay it them same as you would do a real wood floor so the long way not across and real wood is often done in a different direction when it turs a corner to go into another space.

Standard installation practice applies to landing also. Lay the floor boards perpendicular to the floor joist. Whether you decide to use single lengths or mixed lengths is a personal preference. I like waiting until the end of the project to do landings and put in whatever is leftover.