Translation:The political parties make a lot of promises in the election campaign.
I was marked wrong for "the political parties promise many things in the election campaign". I'm not complaining -- more, it occurs to me that "multe" as a substantive use of an adjective (ie, "stii multe" means "you know many THINGS") is something that only makes sense to me because the Romans did it. Is that substantive use of adjectives (multe, etc) explicitly taught somewhere in this course? It's more complicated in a language with a neuter.
No, "while" is a conjunction, not a preposition. It must be followed by a clause with a verb. If you want to use it, you need to add more words "while the election campaign is happening" or "while we're in the election campaign".
In any case, you didn't show how your "while the election campaign" uses less words than the proposed translation "in the election campaign".