Are the archangels Gabriel and Michael twins?

Answer 1

No, both Gabriel and Michael are Archangels that were created directly by God and never had a mother or family of any sort. They may be considered twins at least in one respect- Michael stands at the Right Hand of God, while Gabriel is at the Left Hand of God. Here is a pertinent quote from the Jewish Encyclopedia that helps to explain the connection between Michael and Gabriel:

In other passages seven archangels are mentioned, among them Gabriel (Tobit 7:15, and elsewhere). But he is most often mentioned together with Michael, whom he follows in rank. A Gnostic gem bears the inscription in Greek: "Michael the highest, Gabriel the mightiest". The three angels that appeared to Abraham (Genesis 18) were Michael, Gabriel, and Raphael; Michael, as the greatest, walked in the middle, with Gabriel to his right and Raphael to his left (Yoma 37a). Michael stands at the right hand of God, Gabriel at His left. Throughout Jewish literature Michael appears as an angel of a higher degree,

Interestingly enough. Michael and Gabriel are polar opposites when it comes to the 4 Elements of the material world. Here is the understanding listed below:

Michael: Archangel of Fire and the South, seated at the right hand of God

Gabriel: Archangel of Water and the West, seated at the left hand of God

Answer 2

No they are not. No records of such exist.