Electrical – 3-way switch short circuit

The black wire at the bottom of your diagram is the incoming hot feed and goes to all the switches. If the timer switch has a terminal screw, hook it up to the new switch the same way it was done at the old. If it has a pigtail lead, you'll have to cut the black wire and wirenut both the cut ends with the pigtail from the timer. The blue wire or terminal on the timer goes to the other black wire (the non-doubletap one) going to the single switch, and the white wire or terminal on the timer needs to be connected to the bundle of white neutral wires at the back of the box -- you may need to use a length of scrap white wire as a pigtail for this.

Also, the weirdly wired 4-way switch is really a 3 way switch in disguise, and make sure the single black wire's loose end is capped off with a wirenut.

THIS IS A GUESS - This Explanation and diagrams must be confirmed with a tester.

I added this as a comment but I'll go ahead and make an answer so I can post 2 drawings. This is what I think you have going on, I think the original plan was for the circuit to have just 2 switches as classic 3-way, like this:

(Excuse my Paint abilities, NOTE: GROUNDS NOT SHOWN

The Next day, Next week or Next year someone decided to add a 3rd switch, the load end of the original 3-way circuit became the 4-way, like this: This is one explanation for what I see in your pics, but I can't see everything needed. THIS IS A GUESS AT THIS POINT, using these diagrams as a guide you need to test and confirm the accuracy.

The clues that suggest this explaination to me are the white wire attaching to the common screw in your second pic, and in the first pic a white wire nutted to a pair of black wires. The guess is that's the same white wire. A good first test would be to check for voltage where the white joins the 2 blacks, if my theory is correct that will but hot when the circuit is on and not hot when the circuit is off.