Hello Josh,
Hope you are having a good day so far.
See bellow the answers to your questions:
1. "Quantity to Receive" = The quantity that is expected to receive, depending how setup is set this field is automatically updated at the time we enter the Quantity field.
"Quantity Received" = Is the quantity that has already been received, suppose that we have partial receipts we can perform a control between the initial qty set at field qty plus the goods that were already received.
"Qty to Invoice" this field will shows the qty that has been received but has not been invoiced, yet.
"Qty Invoiced" the qty that has been invoiced.
2. The Qty Received cannot be changed that the reason is shown as non-editable, you can only undo Receipts from Posted Purchase Receipts.
Field "Qty to Invoice" is editable to give the chance to Invoice less qty's than the qty's that are pending to be invoiced if it's the case. in case we do not perform any change the invoice will take all the qty's displayed at field "Qty to Invoice".
3. "Qty received" is not editable in POrder, in case you want to undo the qty received you need to access to Posted Purchase receipts and select Undo receipt for that Item.
Once you have done this procedure and back to your POrder you will see that Qty Received will be set as blank (if all of Receipts were undo, this always depends how many partial receipts we preform) and field "Quantity to Received" has also been updated with those qty's in order you can start the process again.
Hope shared explanations can help you to move forward.