You not need to show much if you get the 3 month visa without extension if you want the extension you need money in the bank etc basically they are the same. Even with the Child you still need the document from the wife amphur etc but with the Child you need the Child papers. The most important thing with you being married is for me that now you have the RIGHT to your child and your house.
I asked many times since i travel around Thailand ALOT! Camping here and there and staying away sometimes 1 month at the time different places. They do not care where you stay you report the first when you come inside from another country thats it no local travel inside Thailand.
Yes you have to report if you stay IN Thailand 90 days if you not then not report it. If you live in Bangkok not report it as well, if you stay first night hotel let them report it