So I recently bought a 1999. Savage with 37000km on it (around 25k miles). It is in good condition overall but the previous owner left it sit for a while unused and it hasn't seen a knowledgeable mechanic in ages. Bike rides great but there are couple of things that concern me. I'm not sure how serious they are so I need your help.

1) Belt
So the bike came with a new belt installed by the previous owner. When I took it home belt was firmly rubbing on the left side of the rear pulley. It also felt overly tight from what I read about the 90 degree twist technique. So i adjusted the tension and tried centering the belt.
After a short ride i noticed that it floated little bit to the right. Then again little bit to the left. But not touching the edge of the pulley. I assume this is normal because of acceleration and deceleration?
The pulley also moves left and right a little bit.  

2) Oil level
Previous owner said he put exactly 2 litres (2.1 quarts) of new oil in the engine. Which is also what the manual says should be.
When the bike is placed upright the oil covers that little window on the right side of the engine. When I turn the engine on level drops to minimum. After running the engine for about 30 seconds and turn it off oil rushes back to cover the sight glass. After reading few topics on the matter I can't be sure if there is too much oil?

3) Valve clack
When riding cca. 30kph (18mph) in second gear I can hear a distinct sound that can be described as sewing machine. Not an unpleasant sound but there is definite rocker movement. Is that normal?

4) Cant move from first gear at standstill
The most troublesome aspect of riding so far has been the gear change. When I slowly arrive at red light in first gear i pull in the clutch and then attempt to raise the peg to go to Neutral, but I cannot. The lever is stuck in first gear. No amount of force will move it. Is that normal?
When the engine is turned off switching from first to neutral feels featherweight.
Previous owner said that he always stopped in second gear. And it is true: it is easier to just stay in second gear and gently push the peg down to N and roll to a stop. But there are situations where I do need to go from 1 to N.

edit:
5) Petcock
Almost forgot to mention the darn petcock.
So when I bought the bike owner said that the petcock is broken and that it only works in RES position. ON and PRI have no fuel flow.

After reading on the topic here on forum I concluded that it doesnt make any sense. The RES position requires vacuum to flow (as does ON). So if petcock is broken only PRI should work.

So I inspected the petcock little closer and decided to test the vacuum port on the bottom. And it worked. When vacuum is applied I have ON (vac) and RES (no vac) working, but no PRI. So I connected a line to draw vacuum from carburator and the petcock works in two positions.

The question is can the bike be reliably run with these two positions? Or am I looking for trouble?

I am planning to order a new petcock but it will take time here in Europe because replacements are rare and the original costs too much money.

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=1561964431

2.  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.

Use Amazon (not eBay) to purchase a Genuine Yamaha Raptor petcock. Don’t listen to your dealer on this.

Is there a Yamaha dealership you could contact?

Also, out of curiosity, what country are you in?

Yamaha Raptor-660 -Fuel c0ck Assy -5LP-24500-01-00

OILChange
 
liters-1.8    QTS-1.9 (WITHOUT FILTER CHANGE)
liters-2.4    Qts-2.5 (with filter change

So, there has been some new development.
I sourced all the parts I plan on replacing including the clutch gasket.

But today I noticed that the head cover cushion on the left side of the engine is soaked in oil. It doesn't leak but when I get paper towel next to it it draws a drop or two of oil.

Valve covers and everything is dry.
When the tank is removed I will make closer inspection. Looking at engine head schematics I suspect one of the bolts it letting through oil.

ArkansasBrian wrote on 02/29/20 at 10:30:22:


Croatia, born and raised.  
I will try the Yama dealership next week.

armchairbiker  the oil leak on the left side could be coming from the thru bolt on the front of the chrome cap( it also holds the head cap down) or the decomp shaft seal .

Check that through bolt for the head before digging too deep.  You'll see it up inside the exhaust outlet.  Put a small wrench on there and give it just a little pressure.  This stopped my oil seep without even needing to remove the nut, clean the threads and apply RTV.  But do that if simply tightening a little doesn't do the trick.

On the shifting issue, also check the rods that connect the lever to the engine case.  If anything  gets bent, it could cause shifting issues.