I purchased a patch-panel for my home studio, coming with the following diagrams:
My question is about the signal direction. Where are inputs and where are outputs on the first images in the row? Does it merge, or does it split signal?
A patch panel like this doesn't have any particular direction of signal flow. It's just connections. A patch panel like this can split a signal, but you generally can't merge signals with a patch panel.
There are some often used conventions for a patch panel. Especially when there are normals like this one.
The assumption made by Neutrik in the top row configuration is that the top rear plug is connected to an output, say the output from a mic preamp. Then the bottom rear plug is connected to an input, like the input on an audio interface. For the top row, those two jacks will be normalled together, which means they are connected if that is all you plug in. That means if you plug a mic into the mic preamp, you can record into your computer without making any other connections, because the mic pre out and the interface input are connected via the normal on the patch panel.
But if you want to put a compressor inline between the preamp and the interface, you don't have to unplug the preamp from the interface, you can just run a patch cable from the top front jack (connected to the preamp output) to the compressor input. Then run a patch cable from the compressor output to the bottom front jack (connected to the interface input) and your signal chain will be
pre -> comp -> interface. When you plug into the bottom front jack, you break the normal between the top rear and bottom rear jacks, which means they are no longer directly connected.
Set up like that, a patch panel usually has outputs all along the top row and inputs on the bottom that are normalled together. You might have 24 mixer direct outs on top and 24 interface inputs on the bottom so you can record direct from the mixer or break the normal and insert something in between.
The bottom configuration is different. Those are really two different setups, because normally you are not changing connections on the rear jacks. You set them up once and leave them. The front jacks help you change the connections. So if the normal gets broken on the rear jack, that means you aren't really using it as a normal.
The lower left configuration is a splitter. You might plug an output into the bottom rear jack and that gives you two copies of that output on the top and bottom front jacks.
The lower right configuration is just a pass through. That means you are taking connections in the back of your rack and connecting them to those rear jacks to make then available at the front of your rack. Remember the compressor we talked about above? Maybe you have this lower right configuration for the compressor. The compressor is in the rack, so you can't easily get to it's inputs and outputs. So you plug the compressor input to the top rear jack and the compressor output to the bottom rear jack. Now when you want to interrupt the normal between your preamp and interface like in the example above, you run a patch cable from the front top where the preamp is connected to the front top jack of the compressor, and then another patch cable from the front bottom jack where the compressor is plugged in back over to the front bottom jack where the interface is normalled to the preamp.
Now if I wrote that clearly enough, you might be thinking "why can't I just leave the patch panel configured like in the top row and hook up the compressor that way? It will be normalled to itself but that doesn't matter". The answer is, you can totally do that and that's an easier way to run the patch panel because you don't have to flip over the cards in some places and not in others.
Probably (hopefully), you're seeing now that the most important thing about setting up a patch panel is planning it and labeling it. Otherwise, it's going to be more annoying than it is helpful.