Hi SamIAm
For the supplier cards that are not showing I would recommend going into the Supplier's card and ensuring that you do have Report Taxable Payments enabled. If that is ticked and the card is not appearing it would likely indicate that the transactions have not been marked as reportable. I would recommend changing the Filters in the Review Transactions to be All and then go through the supplier's transactions to make them as reportable.
On the ABN issue, just testing that particular ABN in my file, it did appear to check that ABN correctly. I would make sure that you haven't selected ENTER at the end of the ABN and look at retyping that ABN in again. Also, you would need to ensure that the serial number attached to that file (Setup>>Company Information) does has an active AccountRight Subscription.
