Aaah, maids leaving is a pickup process (shown via a timer) that you have to juggle around visitors seeing them. They can be put into stasis, boxed (an action another maid can do) then brought out for pickup to avoid this, though visitors can peek into boxes.
Yes, you'll need to order a maid to handle the clothing. From memory, there's a couple of 'handle all clothing' options when doing the interaction, to help avoid needing to repeatedly do so.
Visitors act a little chaotically when there's no maids around sometimes yeah; they also sometimes do so when they want to enter a room for a reason (and particularly when they're stuck somewhere and want to get out).
No worries, it's good to hear what's confusing/out of place - one of the broad goals for the beta phase is to gradually improve the game's tutorials/manual/intuitiveness ^^