How is Edinburgh in the week of christmas? Looking for some advice!

Hi everyone

I am an international student at a major london uni and was thinking of visiting Edinburgh for a short getaway in my winter break as i have seen very beautiful images of the city clad in snow in winter

1)As someone who would be visiting for the first time, do you all have any advice on what to must see or which time to avoid? I plan to go around 20-21st and come back before 24th december

2. 2-3 days enough for edinburgh and would you suggest to go anywhere else nearby as well?

3. Does it snow in Edinburgh before Christmas?

4. What would you advise for cheap stay and travel? I was thinking taking coach from london and staying in some backpackers hostel kinda place?

5. I am a big fan of one day series and was wondering if it would be nice to go to Arthur’s Seat in this time period?

6. I know Edinburgh is perhaps much more colder so what clothing or precaution would you advice? (I always have cold, London is pretty cold for my tropical body haha)

7. Also how to make friends or meet people in Edinburgh? Is there a social square where people hangout or dance? Would love to meet anyone of you as well!

Would appreciate any help, thanks in advance y’all! <3