Could I use "vostro" instead of "tuo"?
What is the difference?
Yes, you could. "Tuo" is used when addressing informally a single person; "vostro" when addressing with slight formality a single person or informally multiple persons. Both are "your" in English.
they, like, never told us that Suo can be used as "your" as well. I suppose it's a polite form but how am I supposed to know that?
could you say "leggo il libro tuo" also?