On the ticket issue: Compare the prices of RT versus one way. It may be cheaper for you to buy a RT ticket and throw away the return. Getting a tourist visa for Thailand in the US does require proof of return or onward travel. If you don't have a RT ticket then I suggest booking an onward ticket that you can refund. In my case I've done that using frequent flyer miles. Costs me nothing but miles to book and they get refunded when I eventually cancel the ticket after arriving in Thailand.
Beware that you might have a problem with the airline flying to Thailand if you don't have a visa and you don't have a ticket to leave Thailand within the 30 day exempt entry. You may have to book with a 30 day return and then change the ticket. A work-around I've used in the past is to buy a refundable ticket that shows me leaving within 30 days to show and then refund later.
My wife and I were married in the US nearly 25 years ago but never registered it in Thailand. We're now going through that process as we're preparing to move (retire) to Thailand. We had to get our US marriage document certified by the US State Department for international use then send it to the Thai Consulate in Los Angeles to certify it for use in Thailand. The document can then be registered in Thailand. The process may be similar for you in Australia.