You coming here with a Swedish passport gives you a Visa Exemption of 30 days.
You do not pay for anything on arrival, but you will need to show proof of outbound flight from Thailand within 30 days.
You can extend these 30 days at a Immigration office in Thailand, 1900 for another 30 days. But after this, you need to leave.
If you want 3 months in Thailand, apply for a Tourist Visa ( or Non O for Retirement if you are 50+ and fill the other requirements ) BEFORE you come here.
A normal Tourist Visa gives you 60 days when you arrive, and can be extended with another 30 days for a total of 90 days.
unless the mother and father were married at the time of the childs birth, the father has, by law, absolutely no obligation to support the child. But he also has no rights towards the child.
Everything is up to the mother.
Is it morally great?
No.
But it is the law here in Thailand and there is no consequence to him stopping the pay to the mother. And honestly, if the mother does not let the child go to see the fathers family, I think it is halfway justified.