Neon is inert because its outermost shell is complete. Neon is already in noble gas configuration and it will be very difficult to change this, essentially making it inert.
Nitrogen is inert because its outermost shell has eight electrons. Nitrogen's outermost shell only has 3 electrons so it is generally unstable and wants to gain 3 more to be in noble gas configuration.
Oxygen is more reactive than fluorine because oxygen needs only one electron to fill its outermost shell. This is just completely false, Fluorine is the most reaction element there is.
Fluorine is more reactive than neon because fluorine has to lose only one electron to fill its outermost shell. Although fluorine is more reactive, this is because it only needs to GAIN one more electron, not lose one more.