Hello Simon,
ad Q1)
this is exactly how the checker module is supposed to work;
ad Q2)
no, nothing else should be needed;
ad problem)
Please make sure that the Invoice address country MATCHES the VAT ID country.
That is, if you use VAT ID DExxxxxxxx, make sure the shoppers country is Germany. There is a crosscheck for the country given by customer and VAT ID country code.
That is so far the only reason I can think of that may cause the check failure, if the EU VAT ID seems to be otherwise valid.
Btw. does the VAT ID you are using validate at
ec.europa.eu/taxation_customs/vies/ ?
If so, and neither the country crosscheck seems to be the problem, please, send us the example of the ID that does not work as supposed.