Yup...that does seem to be a macerator pump under all that rust. The white hose is the inlet (1.5" ID), coming in from the holding tank, the black 1" ID hose is the discharge that should go to a through hull.
The other two hose coming out of the bulkhead appear to be fresh water hoses...I'm GUESSING there might have been a water heater installed in that compartment.
IMO, the macrerator pump is too corroded to be worth even finding out whether it works...but if you plan to sail in LIS (and based on the replies you got previously, you do), or anywhere in CT, RI, MA or the Chesapeake Bay, you can't use it anyway...you must be out in open ocean at least 3 miles from the nearest point on the whole US coast line to dump a tank legally, so I wouldn't bother to replace it, I'd just toss it.
If you will be sailing offshore where you could dump a tank, you'd put a y-valve in the pumpout line (others might suggest just a tee, I disagree with that)--one side going to the deck pumpout fitting, the other side to the overboard discharge pump and thru-hull.
BUT--if it's gonna be a couple of years before you can go offshore, wait till then to install the y-valve and pump...'cuz lack of use is more destructive to any equipment than constant heavy use. For now, just run your plumbing to leave room for a y-valve and pump that are accessible.
Weinie gave you excellent advice: trace every inch of wiring and hoses on your boat, so you'll not only know what each end of 'em is connected to, but the condition they're in.
What's the make/model/age of your toilet? Marine, toilets, unlike household toilets have a finite lifespan averaging about 10 years--some a lot less, a few a lot more...so if it's anywhere near the same "vintage" as the boat, you'll want to replace it and ALL the hoses. Hoses--whether fuel, water, sanitation, engine or exhaust--only have about a 10 year lifespan...after that they start to become hard and brittle, prone to cracking.
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