Contributions to a DFT frequency bin
A frequency bin 'only' covers the value of its center frequency (+ potential spectral leaks to that center frequency). Is that correct?Is that correct?


No. All frequencies show up in all frequency bins EXCEPT frequencies that are an integer multiple of $f_{\Delta}=f_s/N_{FFT}$ sample rate divided by FFT length. 

In other words a frequency bin is affected by ALL frequencies except the center frequencies of the other bins. 

You need to take into account that the FFT assumes that the signal is periodic with N. For a periodic signal contains only integer multiples of the fundamental frequency.