This is a pretty common problem. A three way switch has 3 posts for connection 2 posts are for the carriers between the switches and one post that is for the line/load. So line side (hot wire) attached to one side of the 3 way and the load side (switch leg) attaches to the other and up to the lights being served. Your problem is the one of the line/load conductors is attached to one of the carrier posts and off course the carrier is reversed also. So it's just a matter of having the right wires on the right posts.
If you want to abandon switch 2 you can simply remove the wires from it and connect the line/load conductor to a carrier then find that conductor in the switch 1 box and use it as the new line/load conductor then connecting it to your dimmer. Be sure and wire nut off and make safe the extra carrier conductors.
The problem is that the next person living in the house may want the 3-way back. So might I suggest you repair the original problem. Then purchase a three way dimmer and leave them both in place.
The problem is, you're trying to solve this problem as a box i.e. you want to do all your improvement in this box. But you have 3-way switches. You need to solve each 3-way switch group as a group.
Indeed, the right 3-way is totally separate from the others, and should not be cross-connected. If your box allowed separators you could even put a separator in there.
Rightmost 3-way
On the rightmost 3-way, this is location is the "remote" and both power and lamp cables come into the other end. That is where the smart-switch should go. Lutron Caseta all operates wireless, and their remote switches don't even use wires, so if you put the remote here you simply won't use the 3-way cable at all.
If you want to use a mechanical switch, then you'll need to follow their guidance for wiring one, which is fairly illogical actually. What it's trying to say is you connect a remote switch between the Caseta's black wire and its blue wire. If the switch is thrown, Caseta treats that as an on/off switch command.
So in this case, the Caseta at the far end would send always-hot on the black wire to this location. That goes to the black screw on the 3-way. From a brass screw goes the red wire, back to the Caseta's blue wire. White is unused. The other brass screw is unused.
The rest of it
The left half of the box is complicated. The top cable goes to a lamp, its wires are switched-hot (black) and neutral (white).
The top left cable has 2 3-way travelers (white and red) and always-hot (black) heading off to a remote 3-way switch.
The bottom left cable is kind of interesting. It goes to the lamp controlled by that 3-way (that's the red wire), and it is also the source of power for the box (black=always-hot, white=neutral).
Anyway, here, you would install the Lutron Caseta master, adding its always-hot to all the wires in the black bundle, and adding its neutral to the neutral bundle. The "Load" would go to the red wire from the lower left cable.
As it happens, the remote 3-way is already set up in an advantageous way, with red and white going to travelers and black going to common and that's already wired to always-hot. So leave the black where it is. Tap red for the Caseta's blue wire. The white traveler is capped off.
Best Answer
The pictures that you link to do not provide enough data to be able to give you specific guidance. Basically all that can be seen from those pictures is which switches are 3-way and which are 4-way. Oh and in addition where crappy back-stab connections are used. Additional pictures would clearly show the back inside of the electrical boxes so that the incoming and outgoing cables in each location could be checked to visualize the way the circuits interconnect between the four locations.
I really recommend that you install the actual dimmer at the location of where one of the end point 3-way switches are located. Ideally you will select the location where there is a neutral wire located so that you can use the Caseta dimmer that has the neutral connection. (I know that there are Caseta models that will work without the neutral connection but with the use of the neutral gives you more freedom on the types of lights that you can control).
From your pictures I can infer that your four way switches are using both black and white colored wires to act as travellers. This is a strong indication that there is not a neutral connection run through the 4-way switch box locations. If a neutral was present it would be far more likely that the wire pairs connected to the 4-way switches would be black and red (or some other color that is not white).
The above observation is the reason that you want to study the 3-way switch locations carefully to see which location has a neutral present. If the power feed is coming to this switching circuit from one of the electrical boxes where the lights are located it is possible that neither 3-way switch box will have a neutral.
On the other hand if one of your switch locations is in an electrical box that already has two or three switch units then there is a high degree of possibility that this electrical box has the power and neutral feed coming into that box.
You should not really have to care what location that you place the actual smart switch from a usability perspective. Any of the other locations will have the Pico remotes and once installed and paired with the smart switch they provide the same level of functionality from any one of your current four switch locations.
The Caseta installation instructions will show how they recommend that you bundle the traveler connections in each electrical box to allow bypass across the two 4-way switch locations. I suggest reading through this multiple times to get a good understanding of how this will work. Also if you do not fully understand how conventional 3-way and 4-way switches work in a multi-switch arrangement I would also strongly recommend spending some time researching that subject. It will give you a much better basis to understand the Caseta smart switch installation instructions.