Is it permissible to retain a gifted piece of land if the giver regrets their gift, and is it permissible to demand an increase in the area during partition to compensate for a difference in land value?

There is no blame upon you for holding onto what your brother gifted you from his land, and he is not permitted to retract it, because you paid the cost of registering the entire land. This is considered a gift of recompense (hibat thawab), and it takes the ruling of a sale. Therefore, your brother is not allowed to retract what he gifted to you, and you have the right to hold onto it, and you are not entitled to demand more than that.