I was also not married to the child's mother when my daughter was born in Bangkok. I just made sure that the hospital included me as the father on the birth certificate. Afterwards I had to confirm paternity at my local embassy in Bkk. With all these documents I then went to the Thai registry office (Amphur). No problem! No lawyer needed. My daughter got both nationalities immediately.
Check if your Thai driver's license has an expiration date. If so, then you can only use it for one more year. After that you have to make it completely new.
A visa is not issued by an agency, but by an official authority. Misusing a visa is a criminal offense and can result in serious consequences, like as imprisonment and deportation. Only fools take that risk.