Why is personal information (DOB, marital status) listed on CVs in Europe and can it be omitted? I find it irrelevant to specify personal information on my CV, and frankly I do not see why they should be listed in academic applications. What is the advantage for the hiring committing to know if I am 18 or I have 17 children, aside from creating a chance to bias the hiring process with personal beliefs. Is it because they want to know that I am a prodigy child who got his/her PhD at 18 years old, or because if I am a 28 years old female married without children I will want children soon and so I will have to take maternity leave? Is this just an influence of the age/status discrimination in Europe where I see at times that  job offers are only open to certain categories of people (i.e.,younger than 30 years old) ?

If I omit this information will my CV be frowned upon? Or will they think I am hiding something? I do not know what I would be hiding because age can probably be guessed from the CV anyway.
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.