UK non-VAT registered UK company buys services from EU - can we pay zero VAT?

[Dmitry_Kishkinev]

We are a small non-VAT registered UK company who buys product development services from a EU company. The VAT status of the EU company is to be confirmed atm (may or may not be registered for domestic VAT, may be not relevant to this query).
Q1: Can the EU company put 0% VAT on invoice we pay?
Q2: Being non-VAT registered in the UK, do we have to pay VAT inside the UK or return/report anything to HMRC?