If you have a DTV visa whether a physical label in your passport or a PDF file sent visa the evisa system and you get a new passport then you just show both passports to enter. Show your visa either in the old passport or the PDF that references your old passport and you’ll get a stamp in your new passport to reflect the 180 days allowed.
If you get a new passport prior to applying for the visa then your old passport is irrelevant and not needed.
If you’re already in Thailand then you need to apply for a Non O visa from your local immigration office. You will need to have a Thai bank account and transfer 800,000 baht from abroad.
I’m not a lawyer, nor an expert in Thai laws, but I’m not sure a listing in the royal gazette would be needed. The requirement for incoming foreigners to write a TM6 (actually previously everyone including Thai nationals) already existed. The TDAC is just a replacement for the previous TM6 arrival/departure card. It’s an electronic version rather than paper.
A few years ago they stopped needing air travellers of all nationalities to need to fill one out and more recently for most border points. However my guess is that law still exists but just wasn’t enforced.
Depending on the actual wording of that law the difference of filing an electronic version (called TDAC) rather than a paper TM6 may not need an amendment.
If your children will be going to an international school then get paperwork from that school and apply for education visas for them. You can then apply for a “guardian” visa. There is a financial requirement of 500k each year for the extension.
There is no financial requirement for your children (other than the school cost).
Your partner could apply for a DTV visa which allows them to work remotely. If they want to hire staff and set up a local company then they’d need to do a bit more research on the set up requirements.
100% it will apply to NZ. Also you really don’t want to be applying for any type of visa from NZ. They charge up to 5 times the price of any other embassy/consulate worldwide.