Mathematica 144 Bytes
This is a pain in Mathematica because so few functions adhere to rules 2 & 3. This answer adheres to rules 1 & 2 and also takes care to do the Capitalization. I couldn't even use the built in
Capitalize function. The basic idea is to find the base 10 representation of the string assuming it's in base 36.
as can be seen by running
which yields a handful of built in symbols, only some of which are functions, and none of which are helpful with string manipulation.
A single function solution that came to mind was:
which translates from Hebrew characters, but as you can see it it violates rules 2 and 3.