Hey Martina —
I don’t think asking for questions in a follow-up email is necessarily a red flag. People get busy (myself included) and sometimes have a day where they are less organized than others. It sounds to me like you didn’t have a bad experience in the first interview and I don’t think a single or even two red flags are much to worry about.
I would imagine the in-person meeting (assuming it is with the same person) will focus on more behavioral-based questions or character questions. It might just end up being a casual conversation. Unless the hiring manager is in HR or an interviewing pro, I doubt she will ask behavioral-based questions. It’s more likely to be that she simply wants to meet you in person to get a feel for who you are, how you carry yourself and have a face-to-face conversation.
Did they pay for your travel to the on-site interview? If they did, that is a good sign they will pay some or all moving expenses. If the travel is on your dime, I wouldn’t count on getting any moving expenses paid for.