Learn English – What does “Let’s be in touch {TIME}” mean

I believe Hermione wasn't certain that Harry was going to have good holidays going by his Uncle's shocking rudeness but still wished him nevertheless.

"Looking after" in the context means that she was looking at Harry's Uncle while wishing Harry goodbye and hence that implied pause ( — er — ) in her chain of thoughts and that in effect gave her that uncertain feeling.

“Making to” does mean roughly what you found in the dictionary. “She's making to run away” is mostly synonymous to “she's about to run away”. The difference is that “about to” indicates that she will run away in the future and doesn't convey how the narrator knows this, whereas “making to” tells us that the narrator sees something that shows that she intends to run away. She may be getting into a running stance, or distancing herself from the narrator. If she's “making to” run away, she might still change her mind, or be prevented from running away. That is, she is preparing to do it, but she might be interrupted either by internal reasons (change of mind) or external reasons (prevented) — in fact here it's a combination of the two (the narrator grabs her arm, and she doesn't really attempt to escape).