There's asking a lot of questions, then there's asking the same or very similar questions constantly amid other somewhat disruptive behaviors. The first is a good thing to see in new staff, the second can really distract others from their work & be really annoying. And it can be such a difficult thing to manage, as you're basically telling someone that they are annoying everyone else while trying not to feel attacked and to take it very personally - floods of tears in meetings like this are hard for both parties to handle!
I have been that new staff member asking too much, interjecting inappropriately, trying too hard to prove I was good by asking what I thought were intelligent questions etc. I have ADHD which wasn't diagnosed until very recently plus I would have acute anxiety probably caused at least in part by the ADHD. This would lead to me behaving in a way that could really get on the nerves of others. Sort of a self fulfilling prophesy, trying so hard to prove myself & pass my probation that I would lose the job because I didn't fit in.
I think you need to sit down with her and have a long conversation about the behaviors that you and others are having difficulties with. I have tended since diagnosis to actually initiate this meeting with my manager, and one of the things I have asked for is that they tell me each and every time I do it and promise not to take offence if they do it a bit bluntly rather than delicately hinting.
Now this new staff member may not have that awareness about the subject, but you could offer to work out between yourselves a mutually agreeable way to do this.. This may be a good time to tell her you realise she didn't have the best induction possible, and at the same time ask her how she can be supported in settling in better. Hopefully she will get on side with this.
But if she denies she's acting inappropriately, get aggressively defensive, refuses to see there's anything wrong, or makes silly excuses, then maybe you might want to reconsider her place on the team?