Ranger fluids and capacities here: Ford Ranger Fluids & Capacities
You can get rear axle fluids with modifier already mixed in.
Modifier doesn't hurt OPEN differential axles, so while you for sure have Limited Slip in a Level II, pre-mixed modifier can be used even it it isn't
Level II may/should have Torsen rear axle, Torsen specifies 75W140 synthetic lube and it doesn't need the modifier since it uses gears not clutch plates, but again it would hurt.
I would use a Reverse Drill Bit and drill out the broken bolt.
An old exhaust shop trick is to heat up the bolt and then press a candle(wax) against it, the wax will be pulled down into the treads and help loosen them.