As this word is followed by a possessive pronoun I think it should have a seond accent on the a but was told to watch my accents!
You are correct, it should have a second accent. It has not been possible to fix those yet, but rest assured, you know the rule!
Wouldn't the palatalization of the ν in this word put the accent on the penult? (ev-yé-nya)
Would 'his manners' work?
Yes, it would and many thanks.
Could this also be "his etiquette" ? I don't see myself talking about someone's politeness.
As an Eng. teacher I would use "etiquette" in place of "politeness" because "etiquette" leans more to a formula of behavior rather than a feeling of kindness to another person.