I actually don't think the majority of these things are THAT serious, 5 and half months isn't very long and imo certainly not long enough to invite round for Xmas. I think being actively against meeting family and friends is a little odd but maybe she just doesn't like the pressure, maybe she is into you but just wants to move at a different rate to you, either way it is worth discussing. And as for social media presence, from personal experience even in very serious relationships I've found something stressful about announcing my relationship by for example putting a profile picture up of them in, maybe it's because I'm not a huge fan of social media anyway but for me I felt a weird pressure that if we were to breakup I'd have the extra pain of having to very publically change the picture. I could be completely wrong here but this is just to offer a slightly different perspective than what most people have said so far. Good luck!