Learn Dutch: We vonden het nieuwe interieur erg knus. - We found the new interior very cozy.

It would go directly after the adjective! You would replace erg knus with knus genoeg. Just like in English, when genoeg modifies an adjective, it is placed immediately after that adjective.

Why is it nieuwe with an -e on the end if interieur is a het-word?

When an adjective comes before a noun, it almost always gets an -e ending. The only exception is when it is a het-word that is indefinite (preceded by een, geen, or nothing). Because this sentence uses the definite article het, the adjective nieuw gets the -e and becomes nieuwe.

Could I use heel instead of erg here?

Yes, absolutely. Both heel and erg mean 'very' when used before an adjective like knus. They are completely interchangeable in this context.

Is vonden used for expressing opinions just like 'found' in English?

Yes! The verb vinden (here in the plural past tense as vonden) is the most common way to express an opinion about something you experience. It maps perfectly to how we say 'we found it...' or 'I find it...' in English.