you can make free items in the webstore where users can checkout without payment. you might have to configure it with some bogus authorize.net settings which won't be needed for free orders but might be needed to enable the checkout process in the store.
We don't have a way to add notes to an order in webstore currently.
For custom data maybe your users could use the company name field to add a shipping number
For user account specific things you could create custom user profiles fields on the user account for the purchasing user for the fedex account etc, then when processing the order you could lookup that information from the user attached to the order.
Hope that helps,
Joe