Do you have a picture of what this cable looks like?
The standard OTG adapter that comes with the S7 should look like this, with just male MicroUSB on one end and female USB-A on the other. No 3.5mm.
It will work as long as the variant you're buying supports band 13 LTE. This means any American version EXCEPT AT&T. Also if it's not from Verizon it will need to be unlocked.
That sounds like a pretty thick case lol. Wireless charging is very near-field and won't work with anything thick in the way, even a very thin cases sometimes have a hard time. You will likely need to remove it for it to work.