Answer #1: You will absolutely want to just add a table to the same database that the inventory table is in.
Answer #2: It's hard for me to answer the second question because I don't know your vision for the screen layout of your shopping cart. And although that doesn't sound like it has anything to do with validation, it very much plays a big role.
Is there a public website that has a shopping cart that is similar to what you are trying to design. Some sites have what looks like an order form where you can fill in quantity, select items from a list, and add many items to the cart at once. Other sites have means for you to navigate and learn about one single item on a page, then allow you to provide quantity and click "Add to Shopping Cart". Other sites may have multiple items on a single page where you can add quantity to one or many of those items then click "Add to Shopping Cart".
My question to you is, which one, or combination of, the examples above best describes your shopping cart ??
Most shopping cart sites use the same method when it comes to checking out or showing the shopping cart. Usually a button that displays all of the items, allows changes of quantities, and a button to complete the order or return to shopping.
There's one little quirk when it comes to validating item quantities. And that's at what point do you want to tell the visitor that there is not enough in stock for their request. Most sites will display "In Stock" next to the item before the visitor even adds it to the cart. The tricky part comes if you have 100 visitors on your site and all 100 want to purchase widget #1. Only you have just 50 in stock. The $1M question is, when do you want to remove the item from being available to another buyer. At the time it's added to a shopping cart, or at the time the order is confirmed. If you're OK with the "at the time the order is confirmed", then things are going to get easy. However, if you want to track item availability and inventory during the shopping cart session, that could provide some challenges. Let me explain. You have 1 Reggie Jackson baseball card left. Two people get on your site at the same time. Person #1 adds the Reggie Jackson card to their cart. Person #2 tries to add it to their cart, but your site is validating during the shopping cart session and tells Person #2
Sorry, No Can Do!!. Now Person #1 just realized that he is late for a lunch appointment, closes his browser window (which is an event you won't be able to track with any degree of efficiency or certainty) and heads out the door. Now, you just lost a sale to Person #2.
In my opinion, when it comes to validating item availability in a shopping cart, you display the item availability to the visitor at the time they add it to the cart. Then, you don't recheck until that user confirms the order, at which time you can remove it from availibility in your database. Let me know if that's more down the road you're looking at.
I would love to help you out with this if you can give a few more details about the design and mechanics of your shopping cart. An example from a public website would be helpful as well.
Happy Shopping
ToddWW