Receive vs take

ElidaHe took elementary education.
He received elementary education.

I would include the article: He received an elementary education.

He took typing in his junior year.
(I believe you'd capitalize "Typing," if you intend it as the name of the course.)

The choice between the two is a matter of common practice. It's n

In this case, "took" is more specific or more immediate than "received":

"He took elementary education" suggests that (for example) this year he took (or attended) specific courses within the curriculum of elementary education.

"He received (an) elementary education" suggests a final result or achievement over a longer period of time.

There is also another possible use of the second phrase exactly as it's written, but it requires more qualification:

He received elementary education in the use of computers. This means that he was given some basic instruction in how to use a computer.

What about nationality?

He received/took/gained/ a new nationality?

I'd say "acquired" or "assumed."

If it's in addition, "gained",

if it replaces then "assumed".