Bear in mind that the information I'm giving you is for the Torsk.
For starters, yes, the fresh water system can be used without involving any potable water tanks. As Darrin said, the fresh water header was supposed to be charged to around 8-12 psi, so, when you hook up shore water, you should install a pressure regulator to knock down city water pressure. Otherwise, you may find a few leaks. We use the fresh water tanks #1 and #2 during the winter, because the water to the pier is shutoff during the winter to prevent the water pipes from freezing. Be sure your hoses/pipes are heat traced and well insulated or you may suffer that fate. So far, we've never had the fresh water tanks freeze. If we did, the oncomng ice ager would give us more to worry about than a frozen potty water tank.
You may find that the shutoff valves for the potty water tanks leak. They sure did on Torsk. So, even when we didn't want to use the fresh water tanks, they filled up anyway. Before we began using the tanks, we filled and drained the tanks a coupe of times to clear out any bad water and other contaminants.
Fresh water tanks #1 and #2 are about 980 gallons. Tanks #3 and #4 are about 973 gallons. (I feel like I'm sitting for my qual board). There are two shore connections on Torsk: one is located in the After Torpedo Room on the stbd side about mid-compartment; the second connection is located in the Forward Torpedo Room on the aft bulkhead, stbd side. The Reserves put in a external shore connection in the Forward Torpedo Room when she was a Reserve boat. This line came down through the salvage valve penetration. It allows us to connect city water topside. A copper pipe runs down through the salvage valve penetration and connects into the shore connection in FTR. This is the line we are currently using. Much easier to use than running a hose to the connection in ATR or FTR.
Our San #2 has a sewage pump installed in it along with a high level alarm. A sewage hose is connected from the boat to the sewer line on the pier. When we want to pump San #2 we open a couple of valves and pump. (Except lately, because our sewage pipe was wiped out in a storm.) As for San #1, the honey dipper comes out on the pier and sucks the tank out. We do not presurize the tank. I highly recommend against this unless you like the smell of sewage in the morning. Ask anyone who has blown sanitary on himself. We have found that it was very easy to connect into the blow line for the sanitaries and use that connection for pumping. It eliminates the need for removing the SAn Tank access cover every time the tank needs pumping. It will require a confined space entry to make the connection to the blow line in the ballast tank.
The large spigot on Forward battery is probably the fire hose connection off the Trim Header. Since the Trim Header was normally filled wiith salt water I doubt it was used for filling buckets. Of course, the only reference I have for the valve you are talking about is Torsk. However, the valve you refer to is in the exact same location as our fire hose connection. If you look around, you will find similar connections along the port side in every compartment.
Hope that all helps. If I were you, I would hand over hand the piping in the Fresh Water system and make a drawing that shows all valves and tanks. We did our drawings in Visio. Since you may not have Visio, I converted them to pdf. Note that connections and piping that is not original, like the connections to our hot water heater in the after battery well, are shown in red.