Hi 'Felt' and welcome
It's not too clear from your photos, but that looks like the 'Jabsco' water circulating pump.
It's job is to circulate 'Raw' - canal - water to cool the engine, or to cool the 'Fresh' water in the engine via a heat exchanger, in the same way that air cools the radiator, that cools the water in your car. If you have a pressure cap then yours is probably the latter.
Check out this video for details of how it works
https://www.xylem.com/en-us/support/video-library/jabsco---how-does-an-impeller-pump-work/If the leak is between the pump housing and the cylinder block then it's the rear seal, looking at the setup it'll be hard for a novice to sort it out in situ, there are service kits and spares available on the web but be aware there are umpteen different sizes and as many different drive shaft types.
The pump will leak more with the motor running, mainly due to the pressure it's creating
Best bet is to get someone in a boatyard to sort it, whilst it may seem expensive, given the longevity of the pumps and the aggravation of 'learning as you go' it'll be cheap at twice the price! Jabsco impeller pumps (and their clones) are used worldwide and are almost infinitely rebuildable.
As for the motor it's hanging off, I have no idea! With a bit more information and a few more comprehensive photos I'm sure someone on here will identify it. Which ever yard to choose to do the repair will certainly know. Once you have that information, along with pump and impeller details fan belts, filter types and makes record it in the barges log. It'll save hours later.
Same as above for the pressure cap....
Cheers
Stef