Hi Billy (I assume),
Could you do me a favour please?
Could you click Settings (right at the top),
then Edit Profile (on left)
and put your first name in the Real Name field
and where you are (roughly) in the Location field,
then click the Save Changes button below and to right,
this helps everyone give you more personal and relevant answers - thanks in advance.
Regarding your use of the Fn button, I wonder how you set it?
For the D7100, there are two possibilities;
"AF Lock Only", which (apparently) holds AF while you hold Fn down (but may not disable shutter release AF).
There is also "AF-ON", which is the one you want, this should disable shutter button half press AF.
Do note however, that if you have AF-ON and are using it correctly, you may be misled in to thinking it is refocussing because half pressing the shutter button still starts up the VR in the lens.
As someone mentioned above, AF-ON is best used with focus mode in AF-C, not AF-A or AF-S - if you're getting a beep, that means you have AF-A or AF-S selected, change it to AF-C would be my advice, then ....
In use; you press your Fn button, wait for it to focus, then let go of it.
However, as previous discussions here at CiC have revealed, not all similar models behave the same way, there can be some VERY subtle (and undocumented) differences.
Also, have you checked whether there's a firmware update that might address this feature? (since it is also not unknown for errors to be released in new cameras)
Also, sometimes, other settings can disable or alter certain functionality - I checked and nothing (on my D7100)
appears to affect AF-ON, but as I said above, not all cameras behave the same way.
e.g. I haven't tried, but setting say Fully Auto mode, the software engineer might have decided that in that mode, the shutter button should do what a novice expects it to and over-rule your AF-ON selection for the Fn button.
Hope that helps, Dave