as far as the oil mixing, it should have its own mixer. You put the oil in one place, the gas in the other and the atv mixes it itself.
Unless-----someone has previously taken the mixer off, then in that case you'd have to mix the oil and gas.
I dont know much about the motor running all bad but, I have a 96 that was sorta the same. It was my dads, it had been setting for years when I got it from him. It didnt want to idle at all and smoked like a freight train, but it wasnt the white smoke your talking about. I just changed the plug with an ngk, went and got the most expensive 2 stroke oil I could find, put a bottle of fuel treatment in, and adjusted the idle ( it was set up so high, you couldnt go into gear without grinding like a drunk chick at the bar )
Some other things I have encountered that you might want to keep an eye open for, check that chain every time before you go riding, I gotta tighten mine up usually each morning before we ride(its about a 10 hour ride of rough terrain...if you dont ride as long on rough stuff, you might not have to tighten as often...keep the tools you need to tighten the chain in the 4wheeler, keep extra plugs with you, check EVERY bolt on that thing. Thats been the biggest problem I've had, not sure why, but I've encountered more loose bolts on this thing than one would imagine. And turn the fuel off when your done riding. I know most people do cut it off, but if theres no leak, some people think its fine. I figured out that if you cut the fuel off on these when your done, they will crank on the first time next time you go riding (whether its a day or a week later) Apparently with the fuel on, enough fuel goes through to have it somewhat flooded for next time. With it off, it cranks fine, no choke. I guess last thing I can think off, would be they are real cold natured little machines. Let it do some good warming up before giving it hell
Sorry to write so much and sorry I'm really not even helping you with your problem. I just know I knew nothing about these and needing all the help and advice from these guys I could get when I got it.