Yes
The opening of the bridge at Nong Khai was the first one but you have to enter Laos with tour group.
There are some crossings to Malaysia open but I have not seen the requirements to enter there for those that are not Thai.
You will not need to show proof of insurance to apply for the 30 day extension.
If you want insurance for personal reasons I am sure you can buy some if you want to.
The 90 day reporting requirement ends on the day you leave the country since is a report of "Notification of staying in the Kingdom over 90 days". See the title of this page and it is the same on the TM47 form.
https://www.immigration.go.th/en/?page_id=1666
You have to apply for the visa on the e visa website (https://thaievisa.go.th/) As far as I know there is no allowance for a multiple entry non-o visa.
You do not have to do anything at the embassy. It is done entirely online a you are issued a stickerless visa by email.
I see no reason for there to a problem with the way the flight number has to be entered.
Only the arriving flight number is required on the Thailand Pass site.
You do not need to do a report of staying longer than 90 days in country if you have left the country.
Your first report will be due 90 days from the day you enter the country after your trip out of the country.
If you have insurance the covers you for medical treatment of covid 19 up to $10,000 you do not need additional insurance. You would only need proof to that coverage.
If insured under Thai social security proof of that would be accepted.
You do not need to get a new under consideration stamp in your passport. The one you have allows you to stay until your extension is approved.
The approval is done by Immigration Division 4 headquarters in Khon Kaen. Your local office does not do the final approval.
The approval will probably be done by the 30th.
You apply for the non-o visa and one year extension of stay based upon being the parent of a Thai.
You will need at least joint custody of your children.
From a post I did this morning on the visa forum.
Source: https://www.gov.uk/guidance/notarial-and-documentary-services-guide-for-thailand#services-we-provide-in-thailand