Carpet Two Direction

To keep your carpet looking like new it should be cleaned with a carpet cleaner at least once a year.
Carpet two direction. Orienting the tiles in the same direction will create a seamless look. It looks like your carpet pattern would not make a difference in layout. Any two carpet tiles facing in different directions will appear to be slightly different colors. I bet no one will notice the pattern change.
The manufacturer recommends how to orient the tiles. This is what i would do. See these three different colors of carpet. Then bring the entry hall stair carpet up to the landing.
Carpet does have a direction usually indicated on the carpet backing. Carpet pile should run in the same direction throughout the house sweeping towards the main entrance. Carpet comes on a roll that s 12 feet wide and runs well essentially to infinity. Due to the nature of the carpet this is the direction it should be installed whether on the floor or stairs.
Ideally you would install carpet on stairs as if the roll were rolling down the stairs. Generally seams should run in the same direction as most foot traffic. Your newly cleaned carpet will look as good as new after being cleaned. Think of it like this.
Although your carpet cleaner looks very much like a regular hoover vacuum it uses water and a carpet cleaning solution to remove dirt and buildup from your carpet. On stairways the pile should sweep down. They are just laid with the nap facing opposite directions. Actually they are all the same color of carpet.