Licensed daycare can have 10-12 kids in their house at once ( rules for certain ages) and it's legal. (which would vary by the state.. All daycares and rules are only state... Not federal).
Some home providers do drop in care... But you would need to set up with them in advance... Do all the paperwork, go through the interviews, etc. And then when you call them saying "are you available tomorrrow or next Tuesday " then they can tell you if they have a spot open that day.
There are daycare centers that do drop in care, and advertise for that. My town of 6000 doesn't have one... But the larger town 15 miles away does.
Rates for daycare vary hugely... Area of the country, town you live in, licensed, home or center. You would need to call around in your town to find out rate averages. Home daycare providers decide what they charge... Jane can charge 30 a day for all kids, her friend down the street also does daycare... She charges 70 a day for infants, 50 for all other kids. ( as an example). It's up to you as the parent to decide which you want to go with. There is no set price.