I believe what you have found for verifying the credit card number is actually just ensuring that the number is a valid type (Visa, Mastercard, etc.) Actually verifying the card and the other information you specified would require a connection to the credit card company. This takes an agreement with the company (Visa, Mastercard, etc.) Included in that agreement is the necessity of complying with the PCI standards at the very least. If you actually get into banking issues (storing money electronically for instance), you would have to follow other banking laws. Creating an online payment system is very high-level coding. You need to be dead-certain you know exactly what you are doing so you don't compromise security. My best advice would be to use a payment gateway system and then just use their API. There are a lot of reputable ones out there (including PayPal but there are other ones that are cheaper) that will allow you to verify the cards through them.
Here is an article on how to integrate payments into an ASP.NET site: