"We are eating a few minutes after midnight."
Translation:Vi spiser noen minutter etter midnatt.
"Few" and "a few" have two slightly different meanings in English. The first implies a markedly small number. The second is synonymous with "some." That's also what "noen" means, "some" or "a few," but not "few." "Noen få minutter" literally translates to "some few minutes," which does not make sense in either language.
My guess would be that "skal" stands for the future tense, while "ete" is another word for eating. In Danish it has connotations with animals feeding on something, or with overeating. I am not sure of Norwegian, but see for yourself: https://ordbok.uib.no/perl/ordbok.cgi?OPP=ete , https://www.naob.no/ordbok/ete_2
Word gender and irregular plurals are separate concepts.
You're right that most (but not all) neuter mono-syllable (IE, only one syllable) words have a plural form that is the same as the singular form. There are exceptions. There are also some masculine and feminine mono-syllable words that are the same in singular and plural.
Here's some examples, and a more in-depth explanation: https://wiki.ucl.ac.uk/display/ScanStuds/Norwegian+Nouns