Can my store be setup like this?

I apologize as I was unsure as to which section to publish my question under.

My client needs something setup to where they can select the number of people that will be attending an art class.

It needs to be setup exactly as this website has it setup. Is it possible to do it with Zen cart?

http://www.paintingwithatwist.com/events/viewEvent.aspx?eventID=61934

You can set the quantity in stock for a "product" (the number of class seats), and disallow checking out if out of stock.

So yes, you can easily do this without custom coding.

If you need a dropdown for the quantity, you would make an attribute for "Select number of seats" as dropdown type option name, with option values of 1, 2, 3, etc. Then when you assign the attributes, you would set a total price for each quantity.

A simpler way to set it up would be to set "maximum quantity" to whatever you want, and set the per-seat price. This will show a quantity text entry box by the add to cart, with a note "Max: 15" or whatever. You would still set the quantity of seats in stock for the class product.

The first page sounds simple enough to setup. When you click sign up for class, it goes to this page. https://www.paintingwithatwist.com/events/reserveEvent.aspx
How can this page be setup? If you choose 2 seats on the front page it then will add on the next page under "who's coming" seat 1, seat 2, and so on.

The last thing I would need to get setup would be the third page or continue to checkout.

Okay, that function would require custom coding, a reworked flow, or both.
There is no built-in "second product page with details" in Zen Cart - you enter the product detail choices on the main product page ("attributes").
Nor is there a facility to select product details when you create your billing/customer account.

You can make textboxes to enter all of the information for your attendees in the main product page, but you cannot require that some be filled in and not others depending on how many attendees are signing up. You would need custom javascript for the function you want. This could all be done on the same class page with js expanding sections. Then when you have the class attendance info complete, you would add to cart, then checkout where the billing info is requested.

There is a "Dynamic Dropdowns" mod in Plugins that would begin to handle the desired functionality, and could serve as a base for customization.
You would also need some version of the Stock by Attributes mod to handle total class numbers, if the number signing up in a group is handled by attributes.

I'll check it out. Thanks

Does anyone know a solution for a dropdown on quantity without using attributes? Just a quantity dropdown with the maximum number based on the stock of the product.

You would need to change the code that generates the quantity box above the add to cart from a text input to a dropdown. Someone skilled in input code creation may be able to tell you how to do it.