You just take both passports. If you have an actual visa it won't be transferred but if you have an extension of stay it will be transferred. Either way if you take both passports you shouldn't have a problem
You won't be able to wire the money out of Thailand without either showing that it was earnt in Thailand or having a foreign exchange transaction certificate for when you bought the money into Thailand
If you have legitimised paternity then you can get the one year extension provided you meet the criteria, one of which is that you have to be actually living with your kids full time. Whether or not you are living with your ex is not relevant as the purpose of the visa is for the care of your Thai child not your ex
Lloyd Turner is correct if you were not married at the time of birth or have not legitimised paternity through the court then you are not even the legal father and cannot apply for the 1 year extension. Many people get custody confused with legitimising paternity so you should check your paperwork
I think you're on an O visa if it's based on being a father of a Thai child. If that's the case you only need 400k in your bank not 800k and it only needs to be there on the day that you apply for the visa, no seasoning required