International VAT

[Zanne]

Hi,
I'm planning to open a small online business based in the UK with Shopify.
Some of the products are going to be produced in the UK and shipped both to the UK and the EU.
Some other products will instead be produced by a dropshipping company with factories in the EU but not in the UK. 
In this case the products will be shipped from the EU to the EU but also to the UK customers.

What would be the scenario if I'll decide NOT to collect VAT from my customers (considering I would remain below the VAT threshold both in the UK and in the EU countries)?
Would I be required to pay any VAT to the EU countries where the products are delivered?
Would the EU customers be required to pay VAT as an extra charge by their government tax office?

Thanks