how would the school know your true relationship to a child? Anyone could seek such a letter from a school for unethical purposes - a birth certificate showing you are the mother and registration at the school should be enough to satisfy that you are in Thailand to care for your daughter in school? You need to hire a Thai interpreter or volunteer to go with you because honestly it’s likely all being lost in translation - or hire a agent to sort out the visa issues it’ll probably save money and headaches
no they don’t and that’s exactly what it will take - so unless you really need a bank account which 99% don’t, you won’t get most Thai banks willing