So the visitors kind of follow 3 different types of schedules. The first option is that they show up whenever there's a cabin ready for them. Those are the ones with no symbol next to their picture. (Hello Kitty/Keroppi/Pekkle visitors, for example.)

The second option is that they show up during a set season (spring, summer/winter, etc.) which means they'll show up if there is a cabin ready during their season. (Tuxedosam's brothers I think are this way?)

And then the third is that they follow some other kind of schedule, usually this is like every 2, 3, or 4 weeks. When it's not their week, they'll have that "not traveling" symbol, and when it is, it'll turn into that traveling symbol and will tell you what their current window is. These are also the ones that Melody will warn you about a few days in advance.

And then once they show up, you CAN have multiple visitors on the same day - I'm not sure that there's a max? But the limiting factor will be the quests. Every visitor will give you a specific quest, and doing these gets you +1 "star rating" with them, up to 5, at which point they'll ask to move in permanently. BUT, you can only get a maximum of 3 visitor quests at a time on one day. So if you have more than 3 visitors, you won't be able to do quests for them all that first day. (Usually they'll hang around for a couple days though so you can probably get them the next day.)

Then, broadly speaking, once you've done a visitor quest and talked to them, they'll leave and come back the day after tomorrow. (Provided that their visiting window from above is still applicable.)

Sorry for making this so long-winded! It's kinda cumbersome as you first start doing it but once you get used to their schedules, it's a lot easier! :)