You want to verify that the PM manages many units in that area and properties that are similar to yours.

For example; dirty hallways and litter around your property is a minor issue that can be corrected pretty easily and the owner will quickly be able to verify this has been completed compared with larger problems like delaying evictions or not turning apartments quickly; these are much bigger, more expensive problems and need to be addressed immediately or the PM needs to be terminated.

Tell them that you are not ICE, but you need to know who is living in your house and verify that they do not have criminal records. 

Trust but verify, verify.

He still keeps access to the online account, assuming he has one (if not, get him one), so he can verify monthly payments are being made.

Then when you do an inspection you can verify what the seller said about the condition. 

Should I have a real estate attorney verify the legality of the BP lease agreement or am I safe to just go ahead and use it?

Also verify the zoning as part of the usual due-diligence on a park to make sure the park is still at least grandfathered in as an MHP.

How I can even verify that the seller has this agreement in place and has the authority to sell the property? 

@Jonathan Anderson Like most others mentioned, looking at their tax returns is one way of verifying their income.