Can the fleet officer give the ship she is on a focus as well as another ship? Or can she not target her own ship and it must be two different ships?

Can the fleet officer give the ship she is on a focus as well as another ship? Or can she not target her own ship and it must be two different ships?

Unless the card says "other" or "another" on it. Then the ship it is on, is a legal target for the effect.
So in this case yes, the Fleet Officer can give a focus token to the ship it's on.
Yep, check out the newest FAQ:
My little support shuttle is getting more and more options showing up....