The motor vibration is normal. Both my XA have that. There are several step by step AR XA refurb pages on the net. Most basic things can be done by the average person. Sounds like you need a new belt. I recommend Vinyl Nirvana http://vinylnirvana.com/
Dave's belts are correct in size and work well. There are many other places to purchase belts but some of them are not correct. I've bought a couple of belts from Dave and I know they're fine. (I am not affiliated with the site in any way) Clean the inner platter and the pulley with alcohol and talc the belt before installing.
The bearing wells both need cleaning and re lubed. Wooden handled q-tips work well for this and sewing machine oil is good for lubrication. There are many, many small things you can do to improve this timeless design. The tonearm can be modified rather easily as well unless it needs a rewire. There are certainly more expert individuals out there that can Help as well. Steve Frosten is a member of this site and has a lot of experience with this table. Another expert is a gentleman named Marc Morin.
I suggest browsing to net for how-tos and to continue to ask questions.
AR XA/Jelco 370 Grado Black2 : Cambridge 551P : HK 3480 : Onkyo 7030 : AR3a : Grado SR80e