Hi Mariette,
The SmithCart module sounds like it would be the best fit for you. Please see the following responses to your requirements:
1. EU VAT Regulations can be enabled at the store or Product level. See the following KB articles:
2. PDF Invoices can be sent to the Customer's from email address from the Store Order Details screen. See the following links for more info:
3. The Cart has several Export options. See the following link for more info:
Exporting Data
However, the exports do not include the VAT number but a SQL Server export from the Smith_Invoicing table can produce this info.
We are also available to program the order export to include the VAT number. If you would like a quote to add this feature, please submit a Quote Request at the following link:
Request a Quote
Hope this helps!