What is "ti" here?
Plural you - like in "you guys"
Yes, and actually it can be omitted simply asking "Diákok vagytok?". The verb tells anyway who you ask.
Will be correct to say "Ti diákok?" (I mean, without "lenni")
No, that is not correct. That weird thing when we drop the verb only happens for the 3rd person (and for the formal you)
Mi diákok vagyunk. We are students.
Ti diákok vagytok. You are students.
ők diákok. They are students.
Thanks a lot for fast response! You are the best moderator ;)