It's curious that the accusative plural is used, but that's the correct way. I found this snippet from Thomas Aquinas, Scriptum super Sententiis:
«non enim erat licitum cibos coquere, nec itinerare».
It was not permitted to cook food, nor to travel.
As for noli; just think of the Italian non+ infinitive, it has the same structure. non cuocere il cibo.
It's like the "Don't!" in English.
If you say "Don't touch it". The verb it still "touch".
Literally they order you to not want to do it. (Do not even think about it!).
Nolo means "I refuse".
Jesus said "Noli me tangere": don't touch me.
Do not even think about "me tangere".
nolo, nolle, nolui are the principle parts of the verb. They should usually tell you almost everything you need to know to fully conjugate a verb. I remember my Latin teacher saying how important it was to remember the parts, even before I knew what the last two were used for.
There are often three or four depending on the type of verb:
The present (active indicative) first person singular - nolo
The present (active) infinitive - nolle
The perfect (active indicative) first person singular - nolui
The perfect passive participle - doesn't have one as there is not a passive for nolle.
EDIT: This seems to talk about the parts in more detail: https://www.thoughtco.com/principal-parts-of-latin-verbs-121418