Unfortunately the answer is no, the widow’s pension doesn’t exsist anymore and if she isn’t at least a Permanent resident of Australia she can’t receive any pension at all. All pension’s are means tested and have a qualification period even the aged pension.
TM30 does not show an expiration date, but your local immigration office may require you to do a new one when returning from a trip inside of Thailand. Always best to check on your local requirements.
You are correct about getting 60 days entry in Thailand as an Australian passport holder, but it is called visa exempt, visa on arrival is totally different altogether, just to correct your terminology.
15 days before or 7 days after the due date, take your passport, a completed TM47 form in blue ink and a copy of your up to date TM30 if required, but always best to check with your local immigration office as it varies from office to office around the country