I think a discussion as to whether or not angels exist would detract from the story. Here are two Bible verses to contemplate:
10 “See that you do not look down on one of these little ones. For I tell you that their angels in heaven always see the face of my Father in heaven. (Mat 18:10 NIV)
Do not forget to entertain strangers, for by so doing some people have entertained angels without knowing it. (Heb 13:2 NIV)
The word Angel and messenger is the same word in both the Greek and Hebrew languages. Two messengers flew quickly …
Retractable Wings:
I don’t know. If sometimes we meet angels but are not aware of it, they must have hidden their wings somehow.
Secrets:
7 It is right to keep the secret of a king, yet right to reveal and publish the works of God as they deserve. Do what is good, and no evil can befall you. (Tob 12:7 NJB)