We just registered our divorce and divorce agreement at local amphur. I ( foreigner) will remain sole custody and sole parental power of our child (thai).

My parents financed land and house for our child (gift).

We have been supposed to move into our new fully furnished home during the next 4 weeks.

Does not happen. Best alternative will be to rent and manage property in best interest of child.

1. How to register child at his home (Tabien Baan) child are the owner of land and house (chanote and build permit)

2. Child still registered at parents home of ex spouse.

Kindly advise

You have sole custody so you are the only one who can move the child. That problem solved. To move child into a house, you also need permission from the master of the house hold of that house, that person is "Chao Baan" in Thai.

Land that child owns has a house on it and child is house owner too, that is all good. Every house has a tabien baan (that's the blue house register book) but a minor (underage) cannot be master of the house hold so it must be someone else (or no one at this stage)

If someone else is chao baan then that person must agree for child to be allowed to be moved into his own house

If no one is chao baan, then owner of the land (or in this case the sole guardian representing the child) must first find someone (adult) who accepts to be chao baan, both go to amphur (lawyer good to have if your Thai is not very good) and update records. Original purchasing receipt will be needed for this to be done on an existing house with no chao baan in (don't ask me why but that is what I was required 15 years ago when I had this problem - rules have not changed)

If there are problems and you (as the child = owners representative) want to remove current chao baan, then you need a lawyer (if your Thai is not very good) and you go to amphur and, simply put, open a "case" to have chao baan forcefully removed. Not a difficult process (because owner of land does have power to do this) but waiting time is long, expect at least 6 months, a year not unusual. You must have someone to put in instead of the oustered chao baan if there are people still in the house hold

Good Luck