We need to know where you are (freezing, plants, water) although it may not be critical. It appears that your pond is holding water. If it is really old, that is surprising. And yes, most new ponds are closed systems and old ones could have just been water run to the pond for fill up and a pleasant trickle for an afternoon hanging outside. You might want to try to loosely connect a hose to any of those pipes and see if they are open somewhere. On the other hand, it would likely be just as easy or easier to replumb the whole system.

Again, if it is really old, then I would expect that nothing works, but who knows. If you could turn water on in the basement, and water comes out inside the pond or actually out of the wall outlet, I suppose you could just use it intermitantly. Or it could be modified to use for refilling.

More likely, everything leaks or is clogged so you retrofit. You put a small liner in the pond. You get a small in pond pump and connect a flex hose that somehow gets around to the back wall where it either connects to the old pipe or a new one with a decorative spillway, outlet. The hassle is hiding the pipe/hose from the pump where it either exits the top of the pond, or exits thru the liner and old pond bowl while maintaining a seal at the liner. If one of the old pipes actually goes into the pond, you might be able to cut it off outside the pond and connect it to the spillway.

Yes, I was suggesting that the house pressure may have been an occasional 'pump'. I was assuming that the water flow was not large and either just trickled down the face of your wall or perhaps poured out of a missing medallion with a mouth or spout.

You said: There's a vertical pipe inside the pond which I presume is for overflow.
I wondered if you actually meant a horizontal pipe that went thru the bowl at the top of the expected water level and would have drained any overflow into a very small stream or plant bed or something.

A retrofit could be very easy and not expensive because it doesn't appear that you need much water flow. I also wonder about the height. From your picture, it appears that water was supposed to flow out from that rectangular hole just above that three or four wide, two layer thick, jutting out section of stacked stone that is only a little higher than your two pots. If water was actually to gush over the whole jut out, then a larger 2000gph (gals per hour) pump might be needed, costing in the $200 range, but if it would be more of a trickle, you could get a smaller pump for cheap from Harbor Freight. You might want to search on 'cliffandjoann' here. They have big old expensive pumps but also little aux. pumps (<$50??) that create side streams that they got from Harbor freight.

BTW, if you don't have fish, you don't really need to worry about flow rates or much of anything. You don't really even need a flow. Run it when you are out there and off otherwise. If you want continuous flow, than Mag drive pumps would be better for considerable energy savings. You certainly don't need to mess with your wall. You might be able to re-purpose one of the existing pipes to get water from in the pond to the wall outlet (although they are probably smaller than a best choice which would more likely be 1.25" tubing). More likely, you could just drape a flex hose from your in pond pump, over the bowl, hidden by a plant or something, and then up along the back of the back wall.

Found Harbor Freight and Cliff & Joann's site! Thanks!

I don't see where your water fall would spill from, although I suppose it doesn't really matter. If it fell onto that outcrop, it would give extra sounds although it would probably spill out the back so I suppose the fall is elsewhere. you never actually said how big the existing pipes are, but if they are 3/4 inch galvanized pipe, for example; that was probably too small for a regular modern waterfall anyway.

I'm not sure that any of us is an expert on algae. I have a long stream and a skippy filter. Look skippy filter up. I am quite certain that my stream is my major filter. I get string algae, but find it generally useful. It doesn't cloud up the water; it just looks green. In my case, it is mostly in the stream. I occasionally remove it with a toilet brush to snag it, or just grab it by hand. People with the pea soup algae try all sorts of things and sometimes they work, and sometimes not.

We occasionally have a poster named waterbug_guy. He has done lengthy study and believes that string algae fights off the single cell (pea soup type) algae. But of course, you have to have some to fight the other type. I think that there is general agreement
that the UV tube device will kill free flowing algae. I have heard that
the uv bulb needs replacement every year or so. You don't really need a filter without fish. Again: I never had a problem so am not much help and many who do, don't always get things solved.

If it were me, I would go one step at a time and get a pump and flex tubing. First, I would quickly pump all the water out and clean the bowl with something and see if you can dry it out while installing your plumbing and spillway or whatever. Then I would fill and run it; scrounge up a few plants (hooked on or supported on something, or find a neighbor or store with a water lily to toss in the bottom) and see if algae forms. If you get pea soup that doesn't go away in a month, then get a UV tube thingie and see if that does the trick.

You could look up 'trickle tower' as a filter device. It is a fairly new idea that I know nothing about. But again, I think it is more for preventing build up of ammonia or nitrates that can come from fish waste. No fish, no problem, I suspect.