It appears that rain water flows along the side of your house from front to back, but it also flows from the hedge towards your house. A heavy rain, therefore is going to overwhelm the stacked rocks. Perhaps a French drain solution would be easiest. A normal French drain is a perforated pipe surrounded by coarse gravel. Water passes around the rocks and seeps into the pipe which transports the accumulated water downhill. In your case, I would install a drain collection box just above the stacked stones with a solid but flexible pipe running downhill from there. Here is a PHOTO. Set the top of the collection box right at ground level. Use a COVER on the lower end to keep frogs and such out and hide that with a flat rock.

You’d put the collection box right next to the house, just before the big rocks/stones start? Is that right? Would I need to do anything additional for that area in the third pic, about halfway down the big rock stack, where mud has pushed out from under the sod?

The first truth is that you can never predict the size of the next rain storm or how frequently the largest ones will come. (You can only speculate about averages and typicals.) If you incorporate a drain, it needs to be sized to handle the largest storms you'll have, or it will fail when they come.

Water needs to run away from a foundation wall as it is capable of causing a variety of troubles. Here, it doesn't look like there is positive flow AWAY from the wall. It looks like the flow runs alongside it. As a slope would run away from the house foundation wall, that same cross-section profile of the grade should continue so that the flow also runs away from the retaining wall. In other words, there ought to be a swale alongside, a few feet away from the house and retaining wall. We can see the difficulty of it, but nevertheless it ought to be there. Sometimes, where there is fast water moving through a constricted area, a flume is used instead of a swale. (A flume is paved swale ... like a concrete trough or similar.)

A main problem here is that the retaining wall is very low. It would be very difficult, or maybe impossible, to create a swale or flume with much water carrying capacity. It would be easier if the wall were taller and if its top course of stone were of uniform slope and without gaps. Hopefully, the illustration will help explain how a taller wall would help. (Your top course of stone is not helping with the pieces being of such irregular shape. A more rectangular shape would be better if you can find some pieces like that.)

If you were able to fix the grade so that downslope runs from the house and retaining wall, the flow of washing water would not be going toward the patio, but away from it. Only rain dropping straight down would wet the retaining wall and that would not be anywhere near the volume that is washing from from above, alongside the house.

View from front for reference.

In the last picture, notice how you don't have the problem around the first window ... grade is sloping away from house. But beyond that grade begins to slope toward the house and toward the patio. If you would raise the height of the retaining wall enough to allow slope to keep running away from house and patio, your problem would be solved.