The easiest option is get your kids Thai passports and you get a Non-O marriage Zvisa then extension. Why delay their Thai passports, it makes things much more difficult as you are finding.
You can apply 3vmonths early but as a visa is valid from the date of issue you will lose 3 months of it's validity. Timing is key to get the best outcome.
Yes unless you convert to the 65k monthly international transfer (income) for your extension from your second year or any year therafter (unless your Embassy does the income affidavit)