Your finish plans seem a bit strange to me. You'd normally use either tung oil or wipe-on poly, but not both, And you'd certainly stain the wood first otherwise you'd just put stain the top of the tung oil.
You've got an ash body, so that will definitely need grain filling if you want a smooth shiny finish as shown in your photo. Grain fill, stain, then apply either tung oil or wipe-on poly.
Tung oil for the back of the neck is fine. Not sure what you mean by 'mineral oil' as that covers a wide range of hydrocarbon oils. It's normally either lemon oil or boiled linseed oil to stop the fretboard from drying out.