Vim Newbie – Python Edit/Compile/Run cycle and integrating py help questions

[Daniel K]

I can't seem to find how to ask Vim to "compile" the current buffer
the way I could in emacs (using c-c, c-c.)  What I'm hoping for is to
run the current buffer, show the output in a split window
(horizontal?) and move the cursor in the buffer to the first error. 
Is there a Vim way of doing things?

Is there any way to integrate some python language reference to be
accessed from within Vim?  Something like hot-key keyword lookup to
the docs.

Is asking for keyword completion in Vim going against the grain of
what Vim stands for?  (Simplicity)

Any suggestions or pointers to where I can find these answers would be
greatly appreciated.  I'm really enjoying the power of Vim!!