Understanding the twiddle factors
You got it mostly backwards, but otherwise OK :)
This can be pretty directly answered by writing down what the Cooley-Tukey FFT's twiddle factor $W_N$ is:
$$W_N=e^{-i\frac{2\pi}{N}}$$
and that's it. For example, in your picture, in Stage 0, you're multiplying with $W_2^0=\left(e^{-i\frac{2\pi}{N}}\right)^0=e^{-i\frac{2\pi0}{N}}=e^0=1$.

So k is the index number of the iteration

No, $k$ is the exponent of your twiddle factors. It goes from 0 to half the size of your transform (in each stage).

From the image is the first stage N = 8 (since there are 8 butterflies) or is N = 2

Stage 0 has subtransforms of size N=2, as you can see. (Also, just write down the 2-DFT's formula and compare.)