i agree about a parent shouldnt be doing that. the parent is at fault. not the religion nor the process.
a conversion is very easy. saying shahadah. no need for ceremony, procedures and such. that is why it is hard to judge against a conversion.
if the consent is by both parties, there wont be dispute in the first place. such as the case, the person is at fault.
not the religion nor procedures. because once the father has converted the child, the muslim authorities' hand is bound whether consent by both parties were reached or not.
the conversion is legal. capacity is discussed in issues or ownership. this is guardianship.
not necessarily. the seller need not own the land as long as he can prove assignment of ownership.