My neighbor is friends with the owner of the house I'm renting and the management company is sending these warning letters and is threating me that I have to leave

Are the complaints legitimate and something against your lease? Please give an example or two.

If you have a lease, you cannot be forced to leave unless it ca be proven you violated the terms of the lease. For the management company to cancel the lease, they would have to send you a formal notice to vacate, detailing the cause of the breach. If you can furnish proof that the grounds are false, you let them take you to court and fight it in court. Then sue the nieghbors making the accusations.

If the complaints are not valid, just answer them and tell them that that complain is not valid, and unless they have proof, to please stop believing false reports.