[2ndround]

Why was the account limited?

First sale on the account (otherwise aged), probably the value triggered it as well.
Change in behaviour or something like that was described in the email.

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Does paypal follow up with the company and check the authenticity or are they mainly checking if the company exists and sells similar products?

PayPal requests the said details for authentication purposes, so the answer to your question Is obvious.

Wonder how guys on fiverr for example can confirm functional invoices which are meant to pass the verification process.
Do you think that choosing the more information about this transaction is a red flag for paypal?

Seen several comments across other forums where paypal seem to be very flexible and understanding that the seller did not have all of the required documents. Which seems hard to believe.