questions about fixed internet

Will I continue to receive two invoices, one from my current provider and the other from BASE for home pack?

No. The invoice from BASE for home pack includes all costs relative to the Internet, the fixed telephony and the comfort services.             
However, make sure that you cancel your subscription and services with your previous provider so they don’t keep on sending you invoices. Don’t cancel your subscription before your telephone number had been transferred.
Moreover, if you rent a telephone it is always invoiced through your previous provider.