A. The tirtham offered after Tiruvaradhanam is the snanaasana tirtham. That is, the tirtham with which thirumanjanam was performed for Perumal. Even if it is mixed with arghya, paadaya tritham, no harm in this. All the tirtham are to be partaken.
B. If Perumal thirumanjanam is done with milk, it can be partaken by us and can be distributed to children, as it is auspicious.
It is not a mistake to prepare a second thaligai specifically for offering to Perumal when the first thaligai was prepared for the children. It is the practice of the elders to include curd along with the second offering (Steamed rice).