They even at times busted telemarketers using databases, much less something grave like this.
Of course you better have a good description and consider that bureaucracy moves at the speed of bureaucracy, somewhere between a snail and a plant.
Also, don't forget that these laws also have requirements on you keeping logs, most of the time 3, 5 or more years. So yeah you have to obey a deletion request when that time is up, not "on request" - that would be illegal in most cases.
In many EU countries birthdate (and more) is public information, btw - my own birthdate is made public by the state itself (on the business registry website), together with my name and residence address. Same for any owner of real estate - be it land, house or unit - names, residence addresses and birthdates are publicly available in the online cadastre.
That is simply not true, not in this very general formulation. What businesses does this statement of yours apply to?
It's certainly not common for an ecommerce site to ask for your birthday on signup.
You picked about the only remaining thing where it's not always a requirement. It's a requirement even there if the transaction is over certain threshold (varies by local law, usually around 10k EUR) or certain categories of items (drugs, alcohol, tobacco-related, sextoys, weapons etc).
Not much help for the American cousins, but this already exists throughout Europe and has done for years .... its called GDPR.
TL;DR : If it is or it is tied to PII (personally identifiable information) you have to: