I'm working on a Magento site which ships products via FedEx. When an order is purchased, it should charge the store's FedEx account, allow the store to print a shipping label, and offer tracking information on the website.
In addition, the customer should also have the option of charging the shipping costs (NOT the product costs) to their FedEx account instead.
Is there an existing extension which has all these features, or one which can easily be configured to use the customer's FedEx account instead?
Inchoo has some interesting article regarding FedEx integration. You can read all about it over on their blog post it covers the default magento FedEx options. Anything more and you will probably need to extend the existing implementation and develop a new module.
Inside the module you can setup your FedEx account for the store and it generally has plenty of needed options. Probably it can't handle your second request, charging the customer FedEx account.
The only FedEx extensions are in Magento Connect which is basically the only place to find and get extensions from other developers.