I think there may be some mis-information.Here's a couple of items you'll want to put at the top of your "TO DO" list.
Notice that the pump discharge hose is only a white, light duty vinyl hose:
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This should be a heavy duty sewage hose or it will (or already has) started to smell really bad. Not a big deal if you have no sense of smell. Also, I notice the macerator discharge hose in your photo is now black. I would do a complete inspection from one end to the other just to make sure there are no surprises (or stinking nightmares) waiting for you.
The second item I see is that the PO has labelled the suction side of the pump as the discharge. Not entirely unexpected as all PO's are idiots, as I think most here will attest to.
The one bad item here is the the cheap plastic valve on the inlet to the pump. It is below the water line and so, is a bad idea if the through hull is open (and your is). Also, you never want a valve here as you will ultimately, at sometime in the future, run the pump for an extended period of time with the valve closed. This will burn out the pump shaft seal after a few minutes. For now, I would suggest wiring the valve open and leaving the macerator through hull closed until using it. Definitely not open as your photo shows.
Nothing life threatening here at this time. C'mon now, admit it, you were starting to run out of jobs to do on the boat and this just fills out the list nicely.
The small diameter white hose from the pump discharge looks like Shields Series 148 or something similar. While it may not be the most odor resistant, it certainly is suitable for the use. I'd rely on Peggie's assessment for this. The black corrugated in the last photo is certainly just a cover for the wiring. The white hose to the right side is probably unrelated to all of this. The intake would more accurately be called "suction" but the labeling clearly calls the valve out for "Macerator Discharge". That is how the system is used … it is a Macerator Discharge system from the holding tank, so I wouldn't find any fault in the labeling. It is NOT a discharge directly from the toilet. For that reason, I don't know why the valve would be a bad idea or an improper valve. Perhaps it is redundant assuming there is a y-valve in front of the macerator pump. You have to open the valve to pump out the holding tank to seawater discharge, which is probably an infrequent operation. The pump is below water line, but it is isolated from seawater on the intake side. I would certainly prefer double clamping but the discharge connection from the pump doesn't appear to have enough length for double clamping. It seems that you would need to rely on the thru-hull valve and double clamping at the thru-hull.
I would expect that there would be a y-valve in front of the macerator pump turned toward the pump out hose normally. I might be wrong about this.
In the previous photos, the labeling is above the thru-hulls. Both of the black corrugated hoses are for the sinks. We see the labeling for the macerator discharge, but we don't clearly see the thru-hull or the white discharge hose. The 2 sink thru hulls are open. The macerator discharge is closed, as it should be. I don't think there is anything uncommon about leaving the sink thru hulls open when the boat is occupied and closing them when leaving the boat. I certainly close my galley sink drain when I leave because it is below waterline, but I leave the vanity sink drain open because the thru hull is above water line.