Questions & Answers about Jeg ser en sovende katt på sofaen.
In Norwegian, se can mean to see (notice/observe with your eyes) and takes a direct object: Jeg ser en katt = I see a cat.
Se på means to look at / watch (more deliberate or ongoing attention): Jeg ser på en katt = I’m looking at a cat / watching a cat.
So your sentence uses ser because it’s presenting what you see.
En is the indefinite article meaning a for common gender nouns.
Katt is common gender in Bokmål, so you say en katt (a cat).
(For neuter nouns you’d use et, e.g. et hus = a house.)
Yes, in many varieties of Norwegian katt can be treated as feminine, so ei katt is possible—especially in speech and in dialects, and sometimes in writing depending on style.
In Bokmål, many feminine nouns can also be used as common gender, so en katt is very common and completely correct.