Learn Hardcore Serbian: Često učim jezik sa sestrom, jer ona uči brže nego ja. - I often study a language with my sister, because she learns faster than I do.

Breakdown of Često učim jezik sa sestrom, jer ona uči brže nego ja.

Why is it učim in one place and uči in another?

They are two different present-tense forms of the same verb, učiti (to learn / to study / to teach, depending on context).

In this sentence:

So:

A few present-tense forms of učiti are:

Serbian often drops subject pronouns when they are obvious from the verb ending, but here ona and ja are useful for contrast.

Why is it sa sestrom, not sa sestra?

Because the preposition sa / s (with) requires the instrumental case when it means together with someone.

The noun sestra (sister) changes in the instrumental singular:

So: