Hi.
Pump size is probably up to you. The pond seems fine with what sounds like not much water movement. Most ponds don't actually need any pump, but I think they sure make life easier. I'll bet the pump you have now uses a lot of electric. For sure there's something seriously wrong if that pump is putting out a trickle. The subject of pumps is vast. There are people who say stuff like a pump should turn over a pond once an hour. So if your pond is 1000 gal they'd say you'd need a 1000 GPH (gallons per hour) pump. Some people say more, some less. But that's totally just a made up number, but it's easy to understand and not bad. Google "pond volume calculator" to find the size of your pond.
For tracking down a leak I start with the falls/stream. Most of the time that's the source. You bypass the falls or just shut off the falls and wait a few days to see if the leak stopped. If it's in the falls you can root around trying to fine the leak, but most often you won't. It's a tricky thing, takes some experience. Normally the falls just has to be rebuilt. Less effort than it sounds, but at least a weekend.
If in the pond I check the pond edge next to see if an area has settled.
Next the waterline will drop to the leak, so it will be at the waterline, assuming you check often and evaporation doesn't draw down past the leak. You check the waterline. With a bare liner, which you seem to have on the sides, you can sometimes see a slight damp bump on the liner that pops up at the waterline. That will be the leak.
Some people say to drip milk into the water and the mild will be drawn to the leak. Sounds good, doesn't work. It would have to be a huge leak for that to work and you could just follow the wet area.
Are those huge rocks I see in the pond?