All wrong. Of course I know that Air Force and Air Defense Force are different entities (Duh, you would know if you thought a little what I wrote!). In case you don't know, Russian Air Force also operates its own SAM systems. In particular, ABMs (it doesn't seem to have S-400s, though, just 53T6 missiles). Those S-400s are Air Defense Force.
And yes, a system this complex can be operated by the rebels. How? By reading the bloody manual. This has come up before on Polish news. There are two kinds of manuals for these systems. One of which is an "operational" manual describing a detailed procedure for actual users of the system, the other amounts to "press this button to launch missile" and is meant for technicians servicing it. Buk system is pretty complex, but it has a TELAR vehicle which is essentially a self-contained SAM platform. Using such a platform, it's possible to go through the whole procedure with a single vehicle, as long as you know where to point the radar (which they did, likely by sight). Indeed, it has been said (on the same Polish news) that the plane went down faster than it would have with a properly trained crew. This meant they ignored (or didn't know) the usual pre-launch procedures, target identification and so on.
TBH, you're underestimating how easy it is to gain a rudimentary understanding of even a complex system. I was able to take off and fly around in DCS: Black Shark after less than a day of just reading the manual and starting at buttons (yes, using the "full realism" setting, without automatic startup). Launching weapons from an F-16 in another detailed sim took me about this long. If you have instructions and can follow them, then you can operate any system you have a manual for. Those years of training? They're required to operate them effectively, that is to say, against other people with years of training. Shooting down an airliner that doesn't even suspect someone could try is a trivial affair that pretty much only requires launching any missile at it.
Yeah, so my mistake about IFF. Didn't think collision avoidance squawks and IFF are the same system. Still, even in case IFF is not reliable, a military TA radar can tell an airliner from a fighter. A missile guidance radar likely can't, but the rebels wouldn't bother with that anyway. Regular troops certainly would check their target before launching SAMs.