Logic eval error: txn index 1, len(group) is 1

General
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4

The issue is that And or Or are not like && / || on Algorand.
All the expressions are evaluated even if the first expression fails (in the case of &&).
In your specific case

        [And(Or(Gtxn[0].xfer_asset() == Int(31566704), Gtxn[0].xfer_asset() == Int(312769), Gtxn[0].xfer_asset() == Int(465865291)), Gtxn[0].asset_receiver() == Global.current_application_address(), Gtxn[1].amount() == Global.min_txn_fee(), Gtxn[1].receiver() == Global.current_application_address()), to_nusd()],

systematically access Gtxn[1] and crashes.

See Noob cannot deploy smart contract - #4 by fabrice

All the conditions are evaluated in order.