You're right about the English translation. The Danish one, though, is perfectly fine. In Danish, one might literally say: I have an education as an economist and one as an electrician. In total, I have two educations. (Jeg har en uddannelse som økonom og en som elektiker. I alt har jeg to uddannelser)
Yes, in the context of university degrees (en universitetsuddannelse) it could be translated as such.
As a native USA English speaker we would never say this in this way. It makes no sense in English. I assume that tager is the correct verb på dansk med uddannelse. In English we likely would say "he is pursuing an education". As I am not certain of the meaning of tager in this context we might also say "he is seeking an education". Min dansk ord bog siger at tage can also be "he is receiving an education." Please clarify the intended meaning for tager in this context.
As many have said, this English sentence is wrong. We can say "he's getting an education". Outside of that, you can't make that noun countable. You can say "he's getting educated", or "he's on a course" or "he's at university", or "he's halfway through a bachelor's degree", or whatever this sentence is actually getting at.
As a native English speaker, "He is taking an education" also sounds odd to me. In the USA, we pay dearly for education. If going to college is free for Danish citizens, then yes - one can definitely take advantage of that educational opportunity. If I had access to free education, I'd TAKE an education too! :)
I doubt it has anything to do with paying for education. We say taking a course, even if we are not paying for it, for instance. My daughter, for instance, took French in school, though I did not pay any more for it than any other tax payer without children, just as a Dane might. Indeed, even as a college teacher, I never heard anyone say "I bought a good education at X." Rather, they say "I got an education," or in more formal circumstances, "I received an education." Of course, Danes pay for their college education as well. The only difference is that the 73% or so who do not go to college pay exactly the same amount for the education of the 27% or so who do go to college as those actually "taking" a higher education do.