no, it's not your home, physically or otherwise unless you have a Thai passport! If you don't have that, then you're a guest, whether it be as a short term visitor, or holder of a NON-IMMIGRANT Visa and get annual extensions of stay.
which one? Has a Thai partner but probably doesn't want to commit to marriage. Possibly a child by his Thai partner, but not willing to make a commitment to a situation of his own doing π€ No mention of his age, but presumably not old enough for 'retirement' visa.
Getting married would allow for a 'Marriage' visa, but a long term Visa based on being a parent to a half Thai child, I've not heard of it.