Would it be possible to arrange a permit and return train ticket to Lhasa from Xi'an in 3 days?
Probably not. The permit usually takes 2-3 days to be issued and you would probably need to find an agent and a group and Xian is not a common place to do this.
Can anyone recommend a hostel where they could assist with the process?
Hostels might be able to assist but this is really something that you need to arrange yourself since there are lots of options - how long, what is included, how many people, etc. Best place to do this arranging is Chengdu or Xining because there are lots of agencies located there and lots of others looking to put together a trip.
Approximate cost of permit/visa and ticket?
There is no way to estimate. You can't simply buy the permit. You must arrange a tour complete with guide and driver and the itinerary must be planned in advance to get the permit. Cost will depend upon the number of days, the number of people traveling together, whether additional permits are needed for your itinerary, whether accommodations are included, what class of service is the train ticket, etc.
You need to do more reading. The likelihood of getting this arranged in Xian in 2-3 days is slim to none in my opinion.
Ruth
