No. Where did I say such a thing? Please don't put words in my mouth.
Yes, depending on the customer's country and the product/service you sell.
I don't understand what you mean. Yes, if you are buy something outside of Europe, there is no EU VAT to pay.
Obviously you can claim back the VAT, either through the VAT returns you submit, or directly, in some cases:
This page deals only with refunds for cross-border transactions – where the VAT is incurred by people or businesses not based in the EU country concerned.
taxation-customs.ec.europa.eu
Yes, really. If you have a
US company and you don't even have customers in the EU, but you buy - for example - a new phone for your company in Italy because your old phone got stolen while you were on vacation in Rome, then you can claim that VAT back later. Crazy, I know. Who would have thought.
Just pay for an accountant to handle this for you. Actually, I believe this will be a requirement anyway, as they will require an EU resident contact person for the VAT registration.
Or just don't offer B2C services to EU customers. Simple.