1) Is the JIT standalone? No easy answer. Pypy is a complex project, not just a python implementation. Pypy is a complex toolchain, a framework, for implementing dynamic languages. With pypy, you could write your own implementation of ruby, scheme, php, whatever... And once your interpreter is complete, pypy will generate the JIT automatically for you (you won't need to implement it yourself, you just have to write the interpreter, and pypy will do the rest). Pypy is writen in Rpython (restricted python) but you can implement any vm with it, for any language you may want.

2) How does it compare to c? It's pretty competitive in highly algorithmic code, cpu intensive and numerical tasks. For anything else, it depends. Overall, it on average up to 4 times faster than regular python.

3) Why there's still a difference? Pypy is a work in progress. You should compare it to other projects such as v8 or tracemonkey.

4) Restricted python: It's the static subset of python used to implement pypy. It takes the place of c in cpython. Yes, it's much faster, but also more limited and less flexible. It's nicer than c, but not as cool as full python. You can also find Shedskin and Cython. Shedskin is a true static subset of python that compiles to c++. Cython is a python-like language that adds type declarations to the language to make it closer to c.

Unladen Swallow was a separate project and it's dead now. Psyco is the predecessor of pypy. It is no longer maintained.