I think "brand new" would be stylistically more appropriate, and still carry the same meaning.
I don't think it is appropriate to redraft the sentence like this.
"A brand new bicycle" suggests to me that the bicycle has been built from scratch, probably in a bicycle factory, with new materials and components throughout, whereas "A completely new bicycle" suggests that a total rebuild and refurbishment has resulted in a bicycle that is "as good as new" or even "better than new". OK, I would accept that I am making assumptions here, but, as is often the case with Duolingo's sentences, we really need more information.
I disagree. A brand new bicycle is something I'd buy in a store and I would expect to not have been previously owned by someone else.
You'd need to write "Esta" before "es:"
"Esta es una bicicleta completamente nueva."
As in the previous example English speakers say or write, "It's a new bike". Completely is redundant.
Not really. It could be new for me even though it is actually second-hand, but adding an adjective like "brand new" suggests that it has never been used before.
Actually, the sentence we were given isn't entirely clear, but it is important to recognise when a sentence might be ambiguous.
Having said that, I am not clear what the author had in mind when they decided to use "completely". It does seems too imprecise, but I might give them the benefit of the doubt and suppose that they wanted us to recognise an imprecise sentence, but to go ahead and make the best possible translation anyway.