Yes to the first three questions. I doubt there will be an option to specify matriarchy or patriarchy because you're able to name your heir, so there wouldn't be a need for it.

So as of this moment there are neither a Matriarchy or patriarchy, as CoE don't have the religions and culture we have in real life.

But that can be discussed a bit. Anyway, you can marry whoever you want to, and it's more in the contract you put down things like this, so if it says in your marriage/child contract that you want to take your surname you'll take your surname.

I don't know about inheritance based on sex, since as far as I know you can't decide the sex of your child, which can be quite annoying placing the next child as your heir and then finding out they're of the opposite sex that you wanted, and then you're either forced to give up your title or the sex you wanted to play as (as some clothing are restricted by the sex you are, here mostly just dresses).

Which begs the question, will patriarchies and matriarchies exist?

Neran take the titles from real life with "count/duke/king/mayor/baron" which all have a female counterpart, and often in equal cultures, if they are truly equal, you'll only have 1 word for those things, since sex don't dictate anything.

Not to mention women can wear some clothes (dresses) where men can't? which also begs the question of sex equality in Elyria, if it was truly equality then surely they wouldn't restrict a different way of sewing together cloth to one of the sexes, but who knows what direction they'll go in.

So far I don't know if you can put it down in a contract, but you might be able to write it :P

Thank you for your responses.

The point of being equal in politics and culture, but not in dress is an interesting one - I wonder what the devs would say to that conundrum.