Has your son always lived in Thailand? If your son arrived in Thailand using his Thai passport then these details will be recorded and he will only be able to depart using a current Thai passport
They just need to know where you are staying. If you stay overnight in a hotel they should lodge a TM30, when you return to your own home or rental accommodation then you or your landlord should lodge again. Doesn’t always happen.
I think that your regular doctor will be aware that you do not have any of these, my doctor in Australia just wrote out a certificate for me, no testing required
I got my Visa in Pattaya using Key Visa, it cost me 29,000 baht. I did have the money required in a bank account. If you do not they can help organise this for you.
You can but it will cost you, better to go to Super Rich in the basement and change enough to get by. Super Rich in Bangkok has better rates than the airport