Learn Italian: Lui studia molto bene.

Studia is the "he/she/it" form of the regular verb studiare (to study). To conjugate regular -are verbs for lui (he) or lei (she), you remove the -are and add -a. If you wanted to say "I study", you would use studio.

I learned that Italians usually drop words like "he" or "I". Why is lui used here?

You are right that subject pronouns like lui (he) are often dropped in Italian because the verb ending already tells us who is doing the action. We include them when we want to add emphasis, like saying "He studies very well" (perhaps comparing him to someone else), or just to be perfectly clear.

Sometimes I see molto change its ending to molti or molta. Why doesn't it change here?

In this sentence, molto means "very" and is describing the word bene (well). When it works like this, it is an adverb, and adverbs never change their endings. Molto only changes its ending to match a noun, like when you say molti libri (many books).

Could I say Lui studia molto buono?