Why is personal information (DOB, marital status) listed on CVs in Europe and can it be omitted?
Marital status is completely irrelevant: leave it out. Discrimination based on "Oh, I think you're about to have kids and take a bunch of maternity leave" is illegal.

In practice, date of birth can be inferred from the dates at which you got your degrees and what jobs you've had.  OK, you might be a prodigy who got their BA at 14 and their PhD at 17, but the overwhelming majority of people aren't. Or you might be a total bum who was unemployed until the age of 40 and then got a BA at 43 and a PhD at 48 but, again, the overwhelming majority of people aren't that, either. So including your date of birth doesn't really say anything that the recruiter couldn't guess.

Age discrimination is illegal in the UK, and I'd assumed it would be EU-wide. The usual form would be to require somebody to be within so many years of their PhD, though even that's not-really-so-indirect age discrimination.