Learn Turkish: Ben bile çalışıyorum.

In Turkish, the word bile (meaning 'even') always comes right after the word it emphasizes. So to say 'Even I', you put the pronoun first, making it Ben bile.

Usually we drop the pronoun 'I' and just say çalışıyorum. Why do we need Ben here?

You are right that pronouns are usually dropped! However, when you want to emphasize the pronoun, like pointing out that even I am working, you have to include it. Without Ben, the word bile wouldn't have anything to attach its meaning to.

How does the word çalışıyorum break down into 'I am working'?

It starts with the verb root çalış- (work). Then we add the present continuous tense ending -yor (meaning '-ing'). Because çalış ends in a consonant, we need a buffer vowel before -yor, which becomes ı due to vowel harmony. Finally, we add the personal ending -um (I) to get çalışıyorum.