Could the subject Tu be dropped in Latin? (As long as one conjugates properly? )
Just like we can do in Spanish?
Yes, exactly like in Spanish!
Gratias tibi ago.
Personal pronoun can be dropped, but verb should be at the end
Not only can you omit subject pronouns, you should in most cases. The only reason not to would be to emphasize it.
What is the difference between est and es?
Est is he she it and es is you