The card says:

The Targaryen player may either :

a.) destroy one Dragon to move any dragon strength token from the round track to the dragon strength box or

b.) place a destroyed Dragon in their home area (if able).

Does this mean they have to perform 1 of the 2 actions or that they can choose to to do 1 of the actions or neither (do nothing)?

Yeah this is really not worded properly... But IMO as the card says "may", it is optional. If not, wouldn't it say "must either"?

I thought a dead dragon was out of the game for good!
But with this, then a dragon can come back? Is it possible in any other way?