We say in our area "We have a lot of questions over the menu" Why is this not accepted. Over is used to provide a sense of review.
So, I cannot tell if Duo accepts "vele vragen" as a valid answer here but here is my understanding.
"veel" is not an adjective but a determiner, therefore it inflects for indefinite/definite usage not based on the gendered/neuter distinction as adjectives do.
As a native English speaker who would use this sentence in context I feel as though "vele" is incorrect here (although it would probably be acceptable in standard Dutch - https://onzetaal.nl/taaladvies/advies/veel-vele) because I would argue/interpret it as he has many indefinite questions (veel vragen) and not a list of many specific questions (vele vragen).