(My Tagalog is bad so I understood only some, so I answer in general.)
When the child is younger than 7, then the mother get the custody alone automaticly. except if a court find her not fit as a PARENT. (It's risk drug adiction can be found a reason for that.)
Undepending of who get the custody, the other parent have visitation rights (as long as not have behaved to bad so it become risk for the child).
Undepending of who have the custody, BOTH parents are suppoused to support the child finansialy.
Above is valid as long as no documents are signed to make OTHER agreement volontaringly, so DON'T sign such. Specialy DON'T sigh adoption agreement if wanting to keep contact and the adoption agreement include that IN WRITING including stay living close enough to make visits possible for poor.
In common adoption the child can even leave the Philippines WITHOUT the other parent need to agree, but without adoption the other parent can stop such leaving by not agree.