yes
The word eternally is an adverb. It means to do something for eternity.
The prefix of "unending" is "un-".
I'm not at all sure that there is such a thing. You may have read a definition, starting with "infinite: adjective", and concluded that 'infinite adjective' was the thing being defined. The word infinite is an adjective.
Unending was created on 2007-03-13.
The duration of Love's Unending Legacy is 1.4 hours.
Love's Unending Legacy was created on 2007-04-07.
dumpending
The cast of The Unending Love - 1912 includes: Marion Leonard
Unending, intending...
You have my unending gratitude.
Aeterna
Unlimited, unending