Time to receive zairyu card by mail

Hello,

coming to Japan w/ working holiday visa and I wanted to stay 1 month in a shared house or something, and then find a more permanent place (which I want to see with my eyes before paying).

I read that zairyu cards are usually given out at the airport (e.g.: Narita), otherwise I need to apply at a local office and will receive it by mail.

So two questions:

1. Anyone that has been through Narita on WHV recently can confirm they’ve been given the zairyu card on landing?
2. Any idea of how much time it takes to receive the card by mail? I’m trying to understand the minimum time I need to stay in my short-term place.

Thanks!

EDIT: same question for the national health insurance card, which is only handed out by mail.