My offer would be dependent on the POA being canceled.The owner says he hasn't seen any invoices for any of the work performed from them.

We continued talking and by the end of the call, he agreed to refund our second invoice of $2991, but none from the first $2k invoice.

They have to pay the rent invoice and them come back and make another payment for the late fee.

You'll have an electronic folder with the property name then inside you'll need folders for Purchase Docs, Insurance, Invoices, Financials, etc. 

Is there any late fee if the owner failed to pay some invoice on time?

Enter a maintenance request, assign a vendor, attach a fake invoice.

I think you're options are to use property management software, like RentRedi, or manually send them invoices through a website like Paypal or Stripe.We use Hostfully to manage everything related to direct bookings off of Airbnb.

Enter a maintenance request, assign a vendor, attach a fake invoice.

Can the HOA charge late fees, when I just received my first invoice last week? 

They know i live out of state/county and could practically make up phony invoices for work that never happened.