AFAIK, in EU countries you cannot build/run "your own" billing system. Unless you have a special type of company/enterprise that is accredited and registered specifically for this purpose. This is officially named "Payment Processor".
I think you confuse billing with payment processing, those are two different things. Also there are tons of companies that do e.g. use SEPA direct debit to charge customers (of course relying on a bank to do the transactions), that's illegal now? I think the legislation concerns payment processing services like PayPal and in general any service that processes payments for third parties.
At least in EU, nope! Because it's not just "automation". It's more about dealing with other people's money, accounting, taxation, sensitive data collection etc.,etc. You should be first registered as a "payment processor" type.
You can charge customers by direct debit (bank to bank) with an API. You can create your own pdf invoices and email them. You can charge customers with paypal or use credit cards or any of the EU specific online payment methods.
There is no EU directive or law prohibiting this. You don't need any kind of "special data collection" authorization. Most SMBs just print their own invoices with MS Word or some generic software package.
That's incorrect, at least for some countries in Europe, including Italy (which you mention below).
You can have your in-house billing system (but all the other eu crappy regulations apply, eg. GDPR, VATMOSS), what I think you are referring to is becoming a money transmitter, which requires a special license.
This isn't true. Your own billing system is fine. It's only if you're handling money for third parties - billing for goods or services that you didn't sell - that it becomes a problem. Every single B2B business does not have to be its own "payments processor".
Automated payments in the EU, since the PSD2 law, are no longer possible. Because of the "security" aka TOTP requirement for every activity.
You can become a financial information service or a financial transaction service.
The information service requires the periodic purchase of a certificate and registration with some very annoying hurdles.
The transaction service requires a certification procedure and a lot of money as well as all of what the information service requires.
The EU is a POS. Lobby-created laws that favor the established, rich companies.
It's an elite club and you're not in it, and they're making sure you won't be part of it.
I tried to get information about the information service registration process from the German Bafin, for over 6 months over several mails.
Just tell me what to do, I want to open a financial information service.
They have not given me any information at all.
The employed lawyer kept evading my questions and responded with things that have no reference or meaning in regards to my questions.
I'm not part of the club and they're keeping me from becoming part of it.