Thanks for the welcome BassCliff and baz666!

I'm really happy i found this wonderful place. All you guys are great. So helpful and knowledgable!
So, during the last days, the bike has underwent a major teardown. Here's the verdict: (it's not good, lol)
Compression tests showed an extreme lack of compression on all cylinders, number three had close to no compression, as later discovered due to a valve being stuck open.
The clearance between pistons and cylinder walls is about 0,25 millimeters on all cylinders. Yikes! Cylinder walls and pistons are worn to the extent of it being ridiculous. Compression- and oil rings are almost gone.
One of the valve seats (i think this is what it's called in english) was actually loose in the combustion chamber.
One of the valves were stuck open. I don't know if this is from misadjustment, or if it has simply got burned stuck. There was huge amounts of oil in all cylinders when it was taken apart. Also burnt gunk on all the valves.
A couple of bolts were broken and a couple were missing from the guts of the cylinder head.
Several exhaust manifold gaskets were bad, one completely #"%?.
Exhaust is naturally full of crap, oil and fuel.
So, that was the big scary verdict. Now to the good stuff, that will hopefully see this wonderful bike on the road again soon:
The cylinders are getting rebored as I'm writing this. A brand new, original piston kit and connecting rods have been obtained from Suzuki. Yay!
All the gaskets are being replaced. The top end is getting all the bad valves, seals and seats replaced with new ones. And the broken bolts will be fixed of course
Apart from that, it'll all be cleaned as good as possible, and then to top it off have the oil and filter changed of course. I've been told that I should put mineral based oil in it for now especially, would you guys recommend this as well?
So all in all, it's practically getting a brand new engine

So yeah, there goes the savings, but hopefully after this it'll be ready for the next 100.000 kilometers, I'm counting on having this bike for a looooong time. I'm still a bit nervous that something else will be wrong that I haven't discovered, but fingers crossed that I'll be on the road again soon!
Thanks for all your help guys! I wouldn't have gotten this far without your advice and encouragement!