The hallway doesn't look long enough to need expansion gaps, though I can't see any dimensions. The manufacturer will tell you when you need them. It will be listed in the instructions. They are usually required in very large runs.
For the doors, I use an undercut saw and cut out the frame so the floor tucks under it. For the stairs, I would lay out the full tiles and cut out a cardboard template for the curved area. When it's the correct size, trace the cut on the flooring.
For the doors, I use an undercut saw and cut out the frame so the floor tucks under it. For the stairs, I would lay out the full tiles and cut out a cardboard template for the curved area. When it's the correct size, trace the cut on the flooring.