Getting powers and immediately offing yourself by phasing into a wall

Unfortunately most walls are thicker than 7" when accounting for decorations, furniture, trim, etc. Not to mention adding your own thickness.

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.