What´s the newest Blender I can run on Mac OS X 10.1.5 ?
Why do you want to use 10.1.5?
Anything before 10.2 has performance and bug issues. Panther (10.3) is the best for old machines because it has vast speed-ups. As for compatibility, I don’t know which binaries were compiled for which OS but I would think that you could compile the latest Blender under 10.1.5 and it will run. Did you try the latest version?
If the latest binary didn’t work, I would recommend trying to compile it yourself.