Redox reactions between a free element and a compound

I read that oxidation and reduction occur at the same time when two elements become a compound.
If I am asked:
State the following changes involving oxidation (O) or reduction (R) or neither (N).
F₂ ——> F₂O
F₂ as a free element is 0 but when it forms a bond with oxygen it is F= -1 and oxygen is =+2 which would generally be -2. So, the oxidation state for F is reduced and oxygen is oxidised?
So, in this change, both must be happening. Or, is it specifically asking what is happening to F₂.

I read that oxidation and reduction occur at the same time when two elements become a compound.
If I am asked:
State the following changes involving oxidation (O) or reduction (R) or neither (N).
F₂ ——> F₂O
F₂ as a free element is 0 but when it forms a bond with oxygen it is F= -1 and oxygen is =+2 which would generally be -2. So, the oxidation state for F is reduced and oxygen is oxidised?
So, in this change, both must be happening. Or, is it specifically asking what is happening to F₂.

You seem to have the right idea.
Redox reactions involve a transfer of electrons, so one species must be reduced while the other is oxidised.
In this case, fluorine is reduced (0 to -1) and oxygen is oxidised (0 to +2).

So, would this be considered a half-reaction focused on fluorine because they haven't included oxygen? and therefore be a reduction in fluorine is the only thing observed.
If the arrow pointed the other way, would that be considered a full redox because flourine is oxidised and oxygen is removed by reduction?
Sorry, I seem to be able to find half of the information I want online but not the other.
In most half reactions, they only show one element undergoing a change of charge, not to different elements.

If the question focusses on fluorine (notice the spelling!) then you only need to consider the half-equation involving fluorine.