Not long. Depends on how much air is leaking, but a few mins at most normally until you get the sealant in. Even then, you might still lose pressure until you’ve taken the bike out for a short ride.
Not necessarily the case. I fitted some new tubeless tyres at the weekend to my Swiss summer wheels (not that I'll get the chance to use them this year, it seems) and they held pressure overnight. Lost a little, but they were still at 60psi after 12 hours and with no sealant.
Not long. Depends on how much air is leaking, but a few mins at most normally until you get the sealant in. Even then, you might still lose pressure until you’ve taken the bike out for a short ride.