So accepting and approving multiple applicants is the norm?

Signing the lease demonstrates they agree to the terms and then you can hold them accountable.If you don't do this, then the person named on the lease and paying the rent could disappear and you would have no legal authority to charge the remaining three for unpaid rent.

My application includes an acknowledgment that everything is true and complete.

The only example I can think of is that I asked an applicant questions about their credit report.

Are you not necessarily denying him based on screening criteria - Some landlords make it a requirement to view the property prior to letting the applicant apply.

All things being equal, I would accept these applicants, but I would require them to pay a deposit equal to two months of rent.

While it might feel like an extra charge to tenants, these packages often provide value that indirectly benefits the property owner as well—like reduced maintenance calls or ensuring the property is better protected.In my experience managing a large portfolio of properties, these fees are becoming more common due to the thin margins in property management.

Navigating the Surge in Rental Application Fraud: A Guide for Landlords and Property ManagersIn recent years, the rental market has experienced a troubling rise in application fraud.

Here's a detailed guide on how to screen applicants: Application Screening Guide 

How is PM charging you if the agreement is over?