I'm afraid your shower plumbing is leaking again. Not as badly as before, but leaking none the less. From the looks of things, water getting past the tiles from showering wouldn't amount to much, and would have certainly diminished by now due to lack of use. Continued flow indicates a water source that is not dependent on showering activity.
The reason you are not seeing water on the kitchen side is because the leak is fairly small and the water found somewhere to go that has enough flow capacity such that the water does not overflow across the wall baseplate or subfloor into the kitchen side.
Bear in mind this is just my best guess. Water leaks can be difficult to trace to the source. No matter what, something is not right and needs to be corrected. Even if the source is something else, you need to get into the wall to investigate. Presumably this is easiest from the kitchen side. Would this be how the plumbing was accessed to repair the previous leak?
The easiest route to getting a straight, vertical wall is to identify the furthest out studs and then shim out those studs that are not as far out. Similarly, find the area on each stud that is furthest into the room and then shim the recessed areas of the stud to match.
Shimming can be done using cedar shims, sold by the bundle in big box stores and lumber yards. They can be broken to get the right size and length and tacked in place with a stapler or brads.
Not every inch of the studs has to be shimmed. I would try not to leave a gap of more than about 12 to 18 inches though.
If there is only one stud proud of the rest, I might try to shave that down, but if there are several, proud or leaning, I would use shims.
Getting to 90 degrees is a bit tougher, and is usually only done if there are cabinets that simply must be flush with the side wall. More often the edge of a cabinet near an untrue corner stops an inch or two short of the adjacent wall and is completed with a trim strip.
If you need to get a perfect 90, you can use a framing square in the corner to see where the error is, and which wall needs to be adjusted to accommodate. If the difference is enough, you might even need to rip a thin shimming strip for each stud to adjust, or even sister a stud next to, but proud of, the existing studs as a nailing piece to hold the drywall (sistering is attaching a parallel board of similar size next to an existing board for strength or better positioning).
Best Answer
Can you cut the wall on the other side of the pipes? That might let you get at them without breaking the tile.
Be aware, however, that if you do, it may not help - if the pipes are at an angle, and you straighten them out, you're going to end up with the pipes wanting to come out at a position slightly to the side of where they are now. In other words, the holes in the wall and tile may no longer be in the right position. You may be able to flex things to make this work, but not necessarily.