Hi
I may be wrong but I think 95% of the bike is the same as the TY250. Only really jets in the carb, piston, cylinder head and a few frame mods separate the bikes.
If you cannot find a TY350 manual a 250 one from a similar year will be nearly as good.
A few manuals come up on eBay. Or you may be lucky and get a service CD from the internet with all the manuals including the TY350.
Engine oil: Manual says 800ml but yamaha importer recommended 750ml
Fork oil: 300cm3 (10.6 imperial fluid oz) each - 10w 30 motor oil (normal fork oil feels rubbish so use engine oil)
These measurements are from a 1989 TY250 but they should not differ from your bike.
Hope this helps
Scott