As I've mentioned, I'm no expert. I've never done an outdoor tile project, but I've learned a lot here researching several tile projects of my own and am just trying to pass it forward.
Hopefully there is no internal leak.
Looking at that wall, I seriously doubt there is any plumbing in there, at least on the second floor. My best guess is this is all trapped rainwater and changes in temp etc. make it appear to leak.
What should be the proper fix for this or is it a complete redo.
There is no quick fix. You could try to patch it, but it will just happen again if everything stays the same.
If it cannot be fixed what are the important do's and don'ts on the rebuild?
Start with the correct tile. You want a porcelain floor tile that is approved for outdoors. There are porcelain tiles that look like slate.
I'd do a bit more research on the correct slope. The correct slope will get the rainwater off of the patio right away. It wouldn't surprise me to find after a rain there are puddles on that patio, and that those puddles soaking through the grout and weeping out through the low points on the sides are a big part of your problem.
At the top of this page is a dark bar with a "search" tab on it. If you search for "outdoor tile" or "patio tile" you will find some older threads on similar topics. Anything written by Jazman or Bud Cline is good advice