Yes you will need to leave Thailand to apply and you will need to apply individually ( meeting the requirements individually) as you are not married The children can be dependent on either visa
As you are not buying a condo as an investment ignore all the nay sayers. My parents (Australian) bought a Condo 10 years ago and visited twice a year every year ( as did we) and now they live there happily. And as you said They left it fully furnished with all their things in it every time they left and just returned when they felt like it
No you can't work in Thailand, you can work remotely for another country in Thailand, or go the "soft power " route which is Muay Thai or cooking with extensions every 180 days which would work for you as you would be returning to Australia. Then after you turn 50 get the "retirement" visa