the children being on a house book is very important in Thailand. Without that they will not be able to go to a Thai School, get ID card and many other Thai benefits.
if the father is on the birth certificate you can go to the Thai Embassy in Sweden to obtain Thai Birth Certificates. Then you can get Thai Passports for them. If you do not have time to do that, enter them on visa exempt. Stay on overstay until you get the Thai citizenship sorted. There is no penalty for overstay by minors.
You need to do the citizenship so you can put their names on a house book registration
Don't think the colour of your skin has anything to do with it. The main criteria is native speaker. Many non native speakers command of English is good but their accented English is difficult to understand. Indian call centres a good example.
Having said that native English speakers from Geordie land are not easy to understand 🤣
thanks went on their website and a comparison site I use. Basically to get critical illness insurance you have to start before 65 with all the insurance companies.