I'm in the final week of my PGCE, so hopefully I can offer a bit of insight.
I think most mentors do the absolute best that they can, when it's one of many priorities they have to deal with and it may well not have been their choice to bring a student into the department. It almost definitely wasn't the mentor's choice to have you in for 4 days this term. I do also think (from what I've heard from others) there are mentors and teachers in school who can be unfair to trainees- just as there are also trainees who take the piss or have unrealistic expectations.
I do think OP, that in September when you start teaching classes, you will realise just how busy lunchtimes can be- it's not really a break for the teachers. Your mentor may have duty, be running a club, be running detentions, be preparing for the afternoon (or catching up on other work/admin), be in a meeting or dealing with all sorts of things that you aren't aware of. Also, you don't know what's happened during her day- there were a few days during the spring term where I chose to eat lunch alone because I just needed a bit of time to decompress on my own, rather than chatting to others.
If you're on schools direct, you'll have to deal with your mentor for the rest of the year, and unlike in a uni run PGCE, there's no real outside body who has a high concern for your welfare. Therefore, I think you have to make your peace with the fact your mentor is just "like that" and find a way to work with it.
There will hopefully be someone friendly in the department or school- maybe someone with a bit more time on their hands, who it may be better to go to with some of your questions. For example, as a science trainee, I had a few very helpful technicians who were my go tos for things like "where do I find this room?" and "how does the printer work?" type questions! There was also a lovely NQT in my department who'd just been through the same uni system as me, and she was great at helping me get my head around some of the uni requirements on the course- (I didn't ask, but she kindly offered).
I do think the mentor/mentee relationship can be quite tricky to get right from both sides- whilst they are there to support you, they're also there to challenge you, and ultimately they are the one who can say that you're not up to scratch and need to be put on "cause for concern" or whatever your ITT program calls it. So I do think whilst it can be a friendly relationship, you aren't usually friends.
I do think the first few days you spend in school are always a bit weird- it does get easier! When you're back in school next year, you may find there are other ITT students in school- making friends and being social with them might also help you feel less isolated too!