Learn Turkish: Bağlam belirsiz değil, aksine oldukça anlaşılır. - The context is not unclear; on the contrary, it is quite comprehensible.

No, they serve completely different logical purposes. Aksine means "on the contrary" and introduces a direct contrast that reinforces the first clause ("it's not unclear, rather..."). Gerçi is used to concede a point or admit a reservation. If you used gerçi here, you would expect the second clause to introduce a drawback despite the clarity, such as: Bağlam belirsiz değil, gerçi biraz uzun. (The context isn't unclear, although admittedly it is a bit long.)

Is 'anlaşılır' acting as a verb in the aorist (simple present) tense here?

It uses the aorist suffix, but it actually functions as an adjective in this sentence. It's built from anla- (understand) + -şıl- (passive suffix: to be understood) + -ır (aorist suffix). Turkish frequently uses the aorist form to create adjectives that describe an ongoing quality or capability, much like the "-able" suffix in English. Here, anlaşılır simply means "comprehensible" or "understandable."

What is the grammatical breakdown of the word 'aksine'?

It originates from the Arabic loanword akis (the opposite/the reverse). To form aksine, the word takes the 3rd-person possessive suffix -i (its reverse), the buffer letter -n-, and the dative case marker -e (to/towards). So it literally translates to "to its opposite," which is exactly how Turkish expresses the phrase "on the contrary."

Why doesn't the sentence end with the formal "to be" copula '-dır', like 'anlaşılırdır'?