I don’t know anything about importing pets to Thailand, but most convenient for several reasons is anyway to apply for a 90 days Non O long term visa at your embassy at home before you leave and just do extension of stay in Thailand.
A METV gives you 60 days upon each entry which also can be extended each time with additional 30 days at your local immigration. That’s why you could get up to 9 months in Thailand if you maximise a METV the right way. She can apply for a Non O retirement straight away and need 15-21 days left on her stamp depending on where she applies on a TM.86.
No, you’ll still need to apply for visa before you come, (but you might be included in the possible coming new visa exemption scheme which still is a bit out in the blue).
You’ve maximised two visa exemptions and stayed 120 days in Thailand so far? You could probably do another one without any issues or possible told to get a proper visa next time, the safest option is anyway to apply for a tourist visa and enter by a land border, -unless you use Poipet. There’s a limit of two border entries by land in a calendar year only for visa exemptions.
. You’re entitled to a 30 days free visa exemption and a 30 days extension at your local immigration at 1900 thb. I would advise you to call your airline and ask for their policy regarding onward ticket if you travel on visa exemption. You could risk that they require an onward ticket within 30 days for visa exemption and then your option is to purchase a cheap onward ticket to a nearby destination just to be sure.
Ok, then it’s best and cheapest for you to apply for a 60 days tourist visa before you leave. It’s only approximately €35 and you don’t need to worry about any extension.