Learn Farsi: برادر تو بیشتر از من مطالعه می‌کنه.

This is exactly what the current lesson is about! In formal written Persian, the 3rd-person singular ending is -ad, making the verb می‌کند. But in everyday spoken Tehrani Farsi, that ending drops the 'd' and changes to an 'e' sound. So می‌کند becomes می‌کنه.

Why did we use برادر تو instead of the possessive suffix برادرت?

Both mean 'your brother' and both are completely correct. Using the separate pronoun with the hidden ezāfe vowel (برادرِ تو, pronounced barādar-e to) adds a little extra emphasis to the word 'your'. If you just want to state a simple fact without emphasizing who the brother belongs to, the suffix form برادرت is very common in everyday speech.

How does the comparative 'more than' work in بیشتر از من?

To say 'more' in Farsi, you use the comparative adjective بیشتر. To connect it to what you are comparing it against, you use the preposition از (which normally means 'from'). So 'more than me' translates literally to 'more from me' (بیشتر از من).

Could I use درس می‌خونه instead of مطالعه می‌کنه here?

Yes, but it changes the nuance slightly. مطالعه کردن usually refers to the physical act of reading, researching, or reviewing material. درس خواندن (which becomes in spoken Tehrani) can mean hitting the books, but it is also used for 'to study' in the broader sense of being a student or going to school.