How can the store admin print a PDF invoice sent to a customer for administration?

You can view the PDF invoice from your previous purchases in
Dashboard -> Store sales
Open a transaction and scroll down.
You’ll find a link “Show Invoice” in the “Actions” area

Note: You can’t view the invoice of a purchase older than the activation of the shop styling plugin.

How can I show additional customer information on the invoice (e.g. Company or vat number)?

Create the required checkout field in your wp e-commerce settings (settings->store).
The new field will appear automatically as a placeholder in your toolbar for your mails, invoice and transaction results.