Various visa options dependent on your circumstances. If you are over fifty then ‘non O’ may be your best choice. This you apply for from outside of Thailand. There are financial requirement in order to qualify.
Also, be aware that you can’t work there without a work permit. So, you need to be of independent means.
Technically, no. Your onward journey has to be within your permitted period of stay, which is 60 days. However, they very rarely check. If you haven’t abused the visa exemption in the past then you should be ok.
However, the airline bringing you to Thailand may well check. They can refuse to let you board. Not all airlines check but most I’ve used do.