Connection snaps to the center of the part, instead of to the pin

My first question is have you done a google search of the form “fritzing part 16 channel relay” which turns up this part which I helped someone fix some time ago:

That said, you likely have not defined the pins in parts editor. These two tutorials on making parts (which apply to current versions of Fritzing) may help. Parts making is however fairly complex.

alternately you can upload the .fzpz file for your part (upload is 7th icon from the left in the reply menu) and I’ll have a look at it.

Peter