Great picture!. It would also be helpful if you'd describe exactly what "ports" and water features your pool has. In other words, how many return jets, do you have a main drain, you already mentioned you have a skimmer and sculpture fountain but are there any other possible water items, maybe something that doesn't seem to do anything.
The 3-way pool valves you have, have 3 pipe connections. They are shaped like a T. Connected to the the base of the T is usually, although not always, the input pipe that is feeding pressurized water to the valve, and at the top of the T are the pipe connections to the 2 output pipes that water can flow out of. The handle can be positioned to block one of the output pipes (water won't flow into that blocked pipe, but will flow into the other non-blocked output pipe), or not block either output pipe (water flows to both output pipes equally), or the handle can be positioned to partially block one of the outputs while not blocking the other output. That was a mouthful!
You can also position the handle so the OFF marking isn't facing any pipe, as your picture shows your left hand valve to be. That is the position that allows water to flow to both outputs.
The valve handle has a marking on the part that you don't grab that says OFF. if you position the handle so that the OFF faces one of the pipes, that is the pipe that is closed off from water flow.
Aside from how the valve work, your system takes in water from the pool using the pipe that comes out of the ground and goes to the pump. That is called the SUCTION side of your system. At the top of your pump is a pipe that goes to the filter. That is the start of the PRESSURE side of your system. Every other pipe, valve and piece of equipment that is fed by that is to the left of that pipe, is on the PRESSURE side of your system.
You mentioned your skimmer action is reduced when you re-position one of your 2 3-way valves. That would make sense because you may be closing off some of the flow on the pressure side (by closing one of the valve outputs). It's kind of like putting your hand over your mouth and not being able to blow; because you're blocking the flow. In your case, there will be reduced skimmer action if you block flow on the pressure side of your system.
I am so confused about the pool valves. There are two; the left one controls how strong the jets are.
1. If the jets are full strength, does that mean that the valve is open or closed?
It means you've opened the flow path to the jets by opening the valve to those jets. In addition, if you close valves that feed other items, more water will flow to your jets because it's not being "wasted" on those other items.
2. If the jets are full strength, does that mean the skimmer vacuum is off? Conversely, if the jets are off, does that mean the skimmer vacuum is max strength?
No, just the opposite, If the jets are full strength it's because you're not restricting flow at the skimmer and are able to supply the jets with plenty of water form the skimmer. If the jets are off, it's it's like covering your mouth, nothing can get out so nothing, including the skimmer is flowing water. However, you do have other water paths like your fountain and the unknown pipe in the ground, so there are other factors.
3. I attach a vacuum to the skimmer, should I set the valve to jets full, jets half, or jets off?
Yes, full everything open on the pressure side to so there's NO pressure side blockages. That will maximize the pumps ability to suck. However you probably can ignore the statue and leave it's valve as is since it probably is a low flow device.
4. For normal use, should it be set to jets full, jets half, or jets off?
Generally full on.
5. The right valve controls the water to the statue. I can leave that closed, right?
Yes. That might be the one valve that you partially close to throttle back the flow to the statue. I'm guessing the statue is intended to just have a low flow of water going through it, not a gusher.
I imagine this is ultra confusing. Hope I haven't made it more so.
