If a ship can affect another friendly ship at range 1-3 with its pilot ability (Such as Roark Garnet on the HWK-290 changing a pilot skill to 12 at the start of combat) is the range measured 360 degrees around the ship?

Yes.

Generally yes. You don't have to pick a ship that's in your firing arc, unless the ability specifically says so.

So you can pick any friendly ship with in range 1-3 in a 360 deg arc around Roark. What you can't generally do however is take your range ruler, and rotate it in a 360 arc around Roark to check distances to unfriendly ships. You can only measure from the acting ship to it's target.

Maybe this comment is overkill but the 360 degrees of is measured from the base around the ship as you would measure a target lock for example. Check the rulebook page 9 for this if you are unfamiliar with that.