For OE to AR, the answer is Yes if OE Day end creates Direct batches in AR, and No if OE creates Retrieval batches for AR. You would be able to see the optional field value(s) on the created AR invoice batch prior to posting.

Again, you have to create a 'Batch optional field' in AR9 that has the same title and same optional field type/location as in OE. So the 'Extended PO#' would have to be Text 1 in both places, or Text 2 or Text 3. It cannot be Text 1 in one app and Text 2 in the other.