It is legal for the business that requesting the zoning commission/city council to get a copy of the petition, as it is legal for someone to get a copy of any documents of a court case against them. It is not legal to threaten signers of a petition with a law suit, they have no bases for a suit if the petition does not make fraudulent statement of facts. You on the other hand may have a case for a law suit if they have defamed your name, people will testify to the fact of the statements made defaming you, and they now question your integrity, and you can prove you have been financial harmed.
You will need to speak to a lawyer about this to determine if you actual may have a case.
Yes the petition still has bases of power when the council or zoning board meets.
beware that in many cases like this the council/commission/board will delay a decision , or reschedule the hearing for a future date(which they don't state at the meeting). This is done in hope that witnesses and individuals that want to speak concerning the petition, lose interest and do not appear at the hearing. Often the later date for the hearing notice is given as close to the allowable legal time as possible. This often creates scheduling problems for people that are protesting the zoning change.
Also, you should know that unless homeowners close to business show up at the hearing, sign up to speak(according to the rules of the council or commission/board) to protest--the petition has little weight when there is a counter petition/support aggrement.
If you go to the hearing, just state your reason for objecting the permission. It will carry a lot of weight if you can get someone that signed "your petition" and then signed the other petiton/support letter to speak stating they were threaten with a lawsuit if they did not sign the "counter petition", and they fear that their property resale value will be harmed if the permission is granted, and their right for a quite use of their property will be taken away.
Even if you loose the decision of the council/commission/board, homeowers may still have a case for a civil suit against the business if they can prove lost of property value and/are lost of quite use of their property.