What I can tell you is that it was originally set up to be a twin cylinder oscillator, but it is missing the outboard cylinder and rod.
Yes, that is a feedwater pump for adding water to the boiler under pressure.
It looks like it is probably home-made, or mostly so, but could well have had some possible kit origins too.
With a lot of work, you may have a rather interesting steam plant there, provided the boiler is actually sound.