Python scipy.fftpack.rfft frequency bin mapping
I don't use scipy, but the documentation link you provided is very similar to other real-only FFT's.  So regarding your questions:

1) Note that there is a y(0) in the output, but no Im(y(0)).  That's because for even N and real-only inputs (ie: all imaginary inputs are zero), then both the Im(y(0)) and Im(y(n/2)) outputs are going to be zero, and need not be represented in the output.  So you can't just run a loop from the first to last bin.  And note the difference of output sequence between odd/even numbered N (ie: you have an Im(y(n/2)) for odd N, but it will be zero for an even N). 

2) There is no increase in frequency resolution.  For N complex inputs, the FFT returns N complex outputs.  When the N inputs are real-only, you only need return N/2 numbers because of the symmetry and the knowledge that one or two of them will be zero.

3) No, you'll still be off because of the single y(0) output (ie: no Im(y(0)). See point 1 above.

4) To go from k to F, I just multiply the bin number 'k' by sample_rate/N.  I rarely ever have to do the inverse.

Don't make it more complicated than it is.  Just follow the documentation's description of the outputs.  After doing a few FFT's, you might start doing a lot of that mapping stuff in your head.