It's a tough one because at the end of the day, if you want to go home and things are feeling that bad and unstable then maybe that is for the best but equally, will you regret it if you go home?
I first moved away (to france infact) and I do think it's completely natural to be home sick, espcially the first time and being so far away is bound to be unsettling. It is totally understandable. The best things for me is to not speak to my parents much..if you speak to them all the time you are more likely to miss them/home etc. Keeping busy is good.
As much as I would try and encourage you to stick it out..it is great experience, I think you need to tell the family pretty soon if you intend on going home, so they can make reasonable arrangements. I don't understand why you can't go home for christmas? I feel like that is a reasonable request.
Anyway, whatever you decide, it sounds like there are lots of people there to support you which is good.
Keep posting here if you need/want to.
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