Hello,
ad 1) you can set on what order status, the invoice is generated;
if you talk about case when the invoice was once generated (on confirmed status) and later cancelled or refunded, than it is correct, that it keeps its number
ad 2) this may be related to VirtueMart settings; VM Invoice only takes information coming from VirtueMart; so make sure you have the tax mode in VirtueMart set to EU mode
ad 3) the only reason here I can see that either your VM Invoice is not configured to send emails to both or the shopkeepers email address is not valid or there is some mailing prolem; again, the only role here of VM Invoice is to load the shopkeepers email from VirtueMart settings, compose the email and sent it thorugh Joomla;
if the email to shopper is sent normally, then I think the problem cannot be in VM Invoice (as it send both the email at once, so obviously, they are sent, just the one does not seem to be delivered)