3 and 7. With 3 you can essentially walk through walls, and with 7 you will know exactly which boxes you don't need to check when looking for something.
2x4 studs are 3.5" deep. Even interior walls have drywall on both sides, usually over a half inch, but even half inch drywall, tape, mud, and paint, gets us to 4.5-5" thick.
Very very thin walls, depending on how the 7 inches is calculated (like from your center of mass or from the outer boundary of your form? Do your clothes come with you? Etc)
Only if you're less than 7 inches across in the direction you're teleporting. This is only useful for the super-skinny, otherwise you're going to splinch yourself into a wall.