I have the same model of the 844 - two of them in fact as I like it so much. One was bought new and the other came from auction. It was about the same price as yours but that was something like 6 years ago.
Anyway I have had both open several times. Main problem is the need to service the smoke unit partly because of its vulnerability to AC regulator failure. The one bought at auction also developed an issue with the Pittman motor flywheel rubbing on part of the chassis.
Someone has definitely been inside your engine and did not do a great job of reassembly BUT it's not the easiest thing to get one of these engines back together.
The headlight needs to be re-seated and it's better doing that from the inside lest in doing it from outside you pull a wire too hard and snap it. As you have to open the engine anyway take what I think is the safer course.
Regarding the smoke unit being on and indeed puffing, that should not happen if you have turned the manual switch off. However, in command mode this and other Lionel engines of its vintage had smoke units with heaters that remained on when the Railsounds system was shut down. Thus, there's always a small whip of smoke from the unit even when not running the engine.