Is it true if you have an overnight stay at Kuala Lumpur travelling with Malaysia Airlines the airline pays...?

Yes, only because your flights do not connect and so you have to spend the night in KL. As your Travel agent to call Malaysia reservations or check the fare rules as it should be in the small print. I know this works out of and into Australia because of the connections however make sure your travel agent gets the vouchers you also have free transfers from the airport to the hotel and back. You do not however have a choice of hotel i also believe breakfast is included.