Are Angels Immortal?

No.

Angels will be destroyed at the end of time:

Matthew 25:41 King James Version (KJV)
41 Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels

Below is another verse depicting the Devil being destroyed at the end of time:

Revelation 20:10 King James Version (KJV)
10 And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.