Q1: Do Meteors affect ships with the CD on?
A: Yes
Q2: Do combat attack die bonuses work against a cloaked ship?
A; Yes
Q3: The Cloaking Device card says if a cloaked ship is hit, it loses the cloak and cannot battle back. But if it is not hit, can it voluntarily drop the cloak to battle back?
A: No it cannot drop the cloak and battle back. The ship may only drop the cloak when ordered and can only do so instead of moving.
Q4: Can the unit continue to move up to four spaces through other units as long as it has the cloaking device or is that only for the turn it is placed on the unit?
A: A cloak ship when ordered may move 4 hexes.
https://boardgamegeek.com/thread/2200914/article/31955719#31955719
Cloaked in an Asteroid Field
A cloaked ship can hide, and the way we have played this, is that when attacking a cloaked ship on an asteroid, the attacking ship's one die is reduced to zero.
https://boardgamegeek.com/thread/2574731/article/36694651#36694651