Learn Spanish (Latin America): Mi amigo estudia japonés.

Estudiar (to study) is a regular -ar verb. Because mi amigo acts as "he" (third person singular), you drop the -ar from the end of the infinitive and add -a, giving us estudia.

If my friend is female, does the verb change?

No, the verb estudia stays exactly the same! The -a ending on the verb is used for "he", "she", and the formal "you". You would only change the subject to Mi amiga.

Why isn't the word japonés capitalized like "Japanese" is in English?

In Spanish, the names of languages and nationalities are never capitalized unless they are the very first word of a sentence. So "Japanese" is japonés, just like "English" is inglés.

Why does japonés have an accent mark on the 'e'?

The accent mark tells you to put the spoken emphasis on that last syllable (ja-po-NES). Words ending in -s normally have the natural spoken stress on the second-to-last syllable in Spanish. The written accent mark is needed here to break that rule.