1) Grounding is a punishment where kids aren’t allowed to go anywhere or see friends outside of going to school. The details vary by family and not everyone does it. I don’t think it’s as common as it used to be.
2) It needs more context to be sure, but it probable means to get that spelling word wrong on a test.
3) Wormed there means she kind of pushed her hand into his similar to the way a worm pushes aside the dirt to get where it’s going.
4) Flat there is the idea of exactly two seconds and not a fraction of a second more. The point being it was done very quickly.
5) It’s like the standard idea of putting something in the drawer but it gives the idea that the drawer was a little full and things may have had to be pushed aside or squeezed down a little to make to make room for the newspaper. Toss is similar but the drawer probably isn’t full when you use toss. At least you’re not highlighting that part.