Can the REA amount be based on a quote instead of an invoice? Should the contractor show proof of payment prior to award of REA?
Your goal is to make the contractor whole - not richer not poorer. That is true if negotiating an equitable adjustment before the work is completed or after it has been completed.
You would be considering the current estimates of what the cost would have been to complete the deleted work not yet performed (not the proposal estimates).
They may be providing you a Quote on the work, they did not have to perform because of the REA; however, they should be providing you a formal request for an REA along with the required form filled in from FAR Table 15-2 III.B, column 2 instruction. If they complete the table then this should answer both of your questions.
We encourage you to read the Cost and Pricing Reference Guide Volume 4, Chapter 6 (click the link and hit "Launch Tool") It is an easy read and should help you immensely with understanding how to approach negotiating the REA and specifically what information you may need and how to rely on it.