I would use a company versed in this process to manage the operations of the LLC and collect the rents/operating costs for the owners. 

CPI measures general inflation for consumers for major individual expenses such as food, gas, shelter, and other basics.

On the notice, it MIGHT be legit to just call the money owed "rent".

Are you buying to occupy or rent out?

that way you can utilize a lower downpayment and potentially rent by the room?

If potentially inflation will go up, never pay off debt. 

It sounds like what you are describing is more like someone renting your basement space.  

They are worried about underwriting the deal to today's costs with the concern that rents might not rise to cover the additional costs (keep in mind, I'm in FL with huge insurance rate jumps...but other areas are feeling similar pain).

For due diligence, is it appropriate to ask for records showing current tenants are paying their rent?

Hello-I made a typo on the lease that stated rent would be late after the 10th or each month but it should have been the 5th.