I too own an 850 .22 and a 350 .22 but you have many other nice guns too so I 'm still catching up
You need to visit the 850 forum:
http://www.network54.com/Index/84463
The guys there are pretty knowledgeable and can answer most of your questions but the guys here are right. Umarex is the actual manufacturer. They make guns under the name of Hammerli and Walther, both manufactured in Germany. The main difference we have been able to identify are the "Trade Licese agreement" stamped on the 850 is by 3 different companies depending on when you bought the gun or which batch it came from.
Mine says the following on the right side of the action which is 5 lines in total (by the 8-shot magazine):
"Trademarks licensed by PW International - Germany / Made in Germany by UMAREX cal. .22 (5.5mm)".
What does yours say? If you go to the 850 forum, you 'll see a thread in there somewhere where everyone posted this information, PLUS the S/N which is right behind the bolt. The serial# on mine is: G010097. Yours should be pretty low like in the 8-9,000 range if you bought it more than a year ago. Maybe even G007xxx but I don't think we 've run into any of those.
I agree with you, the 850 is a decent hunter up to 20-25yds but I would not hunt past 25yds with it until after I do the hammer spring mod which gives you another 50-55fps more velocity and even then I will limit it to 30yds at the most. The good thing is, it's very hard to miss with this gun especially with a scope so head shots are easy. It has no recoil and if you hold it steady it will hit the bullseye every time. I get 1 hole shots often at 20yds and usually average 0.25" CTC groups. The problem with this gun is in the winter when you are outside or have it sticking out the window the CO2 gets cold fast and the gun loses power. I will start shooting at targets out the window when the gun is "warm" and it's shoots right on. I also wait about 1min. between shots so the temp. comes up in the cylinder. If I don't have the heat cranked all the way up in the room, and the temp drops like 10deg. the gun starts shooting lower because of the power loss. It can throw you off when hunting if you don't remember that the gun is cold and you have lost 75fps. It doesn't have a lot to begin with. Mine shoots an average of 603-608fps through the chrony at 72-73deg room temp. with 14.3-14.6gr CP, CPH, Superdomes & Beeman FTS. I chronied the gun after I came in from outside (about 35deg out) and it shot 520fps! That is not enough hunting power for 20 or 25yds IMO, not for squirrel or crow anyway. Starlings and mice yes.
Even if the gun is warm and shooting full power >600fps, I would not shoot large animals like a possom, groundhog or racoon with it even if they were at 15-20yds. The 350 is much better suited for "larger" small game and will put their lights out at 40-50yds because it has about twice the energy of an 850.
Umarex did a good job with the 850. Its barrel is super accurate and the gun is well balanced, not heavy and not too light. Still you have to be careful. I do not rely on it for hunting if I have more than 90-100shots on the Co2 cylinder which seem to be all I can get for full-power. From shots 100-160 it seems to shoot about 30-40fps slower, and shots 160-220 shoots at around 500fps which is still good for plinking or 10-15yd target shooting, and then dies off quickly after that. So I make sure I go hunting with a fairly fresh CO2 bottle.
Diana 350 Mag .22
Hammerli 850 .22
A few Crosman CO2 & Pump .177