How important is knowing an advisor prior to applying for PhD?
Super important.
Does an email interaction play a vital role when the department makes its admit decisions?
Sometimes yes. An email + an visit in person to the university could surely increase your probabilities to get accepted.
If email contact is important, can a student send out mails to 2-3 professors (working in the same area) in case one of them does not bother to reply?
Yes, sure, mandatory! Send as emails as you can!
To sum up, is applying of any use (especially in top universities) when you have no contacts and only your credentials to bank on?
Yes, try to contact and visit the professor you want to work with.
