in my experience the tetris matchmaking takes like 30 seconds to start a new match. doesnt feel any noticeably slower than the time between COD matches or something on xbox
For the online mode of Salmon Run, yes.
It's been a few years since I touched Splatoon but from what I recall, if you go to the arcade, you can set up a local co-op Salmon Run session anytime. It is/was not well-advertised.