I know that I can not deny an ESA for a tenant, but can I deny their guests from bringing ESA animals when they visit or stay overnight?

It is a great tax benefit and, as any great benefit, it is frequently abused.

We’ve repeatedly asked the seller to provide the tenant’s rental payment history, but there has been no response.I asked my realtor how we can verify the payment history, but she didn’t directly answer and simply mentioned that I can either accept or deny the lease (it’s a month-to-month lease, which I’m fine with).Should I move forward with the sale?

They can't deny you from entering your own property.

Why does denying agents the ability to show a commission benefit anyone? 

. :)First, I wrote this loooong post on tax strategies and on abusing them.

Just wanted  to let you know simply being a veteran may not be the best thing to deny a tenant. 

Quote from @Denis Ponder: My plan, after I accumulate enough property, is to refinance certain properties each year and collect the tax free "income" from that property and enjoy life. 

Denying entry is a lease violation and grounds for eviction.

In my area it is common for landlords to pay for heat which promotes a lot of abuse with the system in that tenants keep the heat at unreasonably high temperatures and often open the windows in the dead of winter when it can be -20 out.