1. Do I need to use that front screw? This would require making a new hole in my new custom non-factory stock.
No, not needed.
2. Would I need to use this front screw if I chose to have the stock bedded? It seems like it would be unnecessary to use this front screw in that case. An I wrong about this?
Correct, you're not wrong.
3. How do people normally deal with this screw?
You are again correct about this. If you wish to retain the exterior appearance and not have an empty screw hole in the original stock, you shorten the screw and epoxy it in there, then provide clearance in the barrel channel to float the barrel.