Purchases outside the EU for starting my sole proprietor (vAT charged)

Is it a problem that my company number is not stated on the invoices? Should I question them for a new invoice with my company number on it?

If you want to reclaim vAT, then yes. The company number must be on it.

Submitting costs is not a problem.

The invoice is from a non-European company and vAT has been charged. This causes me problems when entering it in Dexxter because it expects the vAT to be reverse-charged. How can I solve this?

Subject to VAT? Then you can simply enter the foreign vAT as an expense.

Exempted from VAT? Then you must submit a special vAT declaration.