Pw80/KX YZ125

The PW can be set up for premix, but it requires disconnecting and plugging the oil injection, not just putting premix in the fuel tank and not putting oil in the injector. That will lean it ou, as air will be sucked in through the injector. Is it worth the trouble? I'd say no, as PW's last a while on a tank of oil, so why not simply make it a habit to refill it once every week or so. Heck even better, teach your son how to do it, so that he checks it before riding and doesn't run it out. It doesn't take long to top it up, which ensures it is full.

As to the oil for the KX and YZ, there actually is no crankccase oil on a 2 stroke bike, that is supplied by the premix/injector. The transmission oil however is a topic of debate. Many use 10-40 motor oil, others use ATF, while others use hypoid gear oil. So long as it is one of these, and is changed regularly, you will be fine.

My trans oil = Mobil 1 15w50 Extended Perfromance.

Since you have probably already lost the little rubber number plate holders, just pull the panel out a little and look at the side of the tank before he goes out. The translucent white of the tank makes it pretty easy to tell how much is in there most of the time. If you arent sure, wipe the dirt off the side of the tank. The PW will go through several tanks of gas before the oil tank runs dry.
I had actually forgotten about this, but there is also a sight window cut intro the side panel, if the tank is dark, there is more than enough oil in it. If the oil level is visible, you still have plenty, once the oil drops below the window, go ahead and top it off.

Just make sure to change every few hours. Some are more worried than others, and change it after an hour or two, but most will say 4-6 hours on it won't hurt anything, some will push it longer. It also depends upon how much you abuse the clutch as well, heavy clutch use will contaminate the oil faster than if the clutch is used relatively little. Just don't try to push it too long and you will be fine.

That's why I forgot the window, I don't use it. I kneel down and lift the panel enough to look under it. Checking it once a month is probably good enough. These things don't use much oil.
I just did a little research, and I think the PW runs at 24:1 from the factory. The gas tank is 1.2 gallons and the oil tank it 1 quart. So you should be able to run 6 gallons of gas through the bike on a single tank of oil. For simpler rememberance, that's 5 tanks of gas, so just check it every 5th tank.