Except where does the engine (or any kind of fuel, gyroscopes, etc.) fit into any of these mecha?
Compartments. Think of the outer mecha as a kind of power suit/armored exoskeleton for the inner mecha. The larger Banshee unit has a lot of space to include generators/engines, but if I gonna nitpick about the design, it's gotta be the structural stress on those lowerside optional arms-link. There's no fucking physically possible way that these thin arms can withstand lifting objects 5 to 10 times more mass than itself, evenmore in high G conditions.
just like ACs most of the important components are stored in the body so I'm guessing everything is connected to it which depending on the spec of the outer part can go either way fuel storage, batteries or ammo
They did this in the Simpsons. The episode where they did an Avatar parody where Chalmers was in a mech suit and jumped in a bigger mech while piloting a mech suit. A real yo dawg moment.