While waiting for the decision on my polygyny application, what are the limits of my relationship with the prospective second wife?

She is still a non-mahram woman to you, so the limits of interaction are the same as with any woman you have not married. ‘Applying’ status does not make it lawful to be alone together, to touch, or to have intimate conversations late into the night. Keep dealings to what is necessary, preferably with her family present. Remember too that the court's decision may not go your way; a relationship that is too close will hurt both of you if the application is rejected. At the same time, your attention to your existing wife is being tested. Do not let her feel sidelined while you are busy with new plans. See limits of aurat and interaction.