Welcome aboard Armchairbiker. In answer to your questions:
1. The pulley wobble will degrade over time and eventually result in all sorts of howling coming off that drive belt. No amount of adjusting will correct the problem. You can permanently fix it for under $20. See this old post for an easy fix.
http://suzukisavage.com/cgi-bin/YaBB.pl?num=15619644312. The oil level can be a sure fire indicator of petcock failure. Fuel leaks past the petcock, needle & seat in the carb, and ultimately down the chute past the piston rings and into the crankcase. The level should be between the two marks on your sight-glass. I suggest you drain and refill to the proper level with the bike perfectly upright. Give the old oil a good smell test for any sort of gasoline aroma. If you think you smell gas you probably have a petcock problem.
3. A moderate amount of clickity-clackity ticky-tacky is normal for the LS engine.
4. You should be able to shift the lever from first to neutral with very little effort. Several problems can cause the condition you describe. Clutch maladjustment or oil too heavy would be what I would look at. Since you will probably be dumping your oil that should take care of any questions about the oil. Replace it with a good quality 10W-40 rated Jaso MA2 and you should be good in the oil department. There should be some good guidance in this forum on clutch adjustment. It should be very easy to move the lever from 1st to neutral with engine idling and clutch lever pulled in.
5. Petcock? There's only one answer for that. Replace it. Don't waste time testing it or trying to repair it. It's gonna leave you high and dry. Even when these vacuum operated contraptions test OK, they still hang up and leak. You will either find yourself stuck out in the middle of nowhere, or go to start up in the morning with six-quarts of liquid in the crankcase instead of two quarts. The stock petcock simply isn't worth all the aggravation. I can't begin to tell you how many motorcycles (various manufacturers) I have repaired over the years as a result of failed vacuum-operated petcocks.
Good luck with your Savage.