Can't see how the skimmer would take formalin out. Also, UV shouldn't be a problem. Formalin is used a lot in commercial aquaculture recirc systems where UV is employed. I have not heard of any problems where the baths are given for an hour and the UV is left on (dose range in the 150-200 ppm). However, water chemistry, dose and your product's formulation may be factors that affect stability. The main concern is whether the UV would cause the precipitation of paraformaldehyde, which is very toxic (but I don't think this would happen).
Not sure about the Phosreactor - depends on the properties of the resin that it uses.
Keep in mind, despite what some may say, formalin is hard on nitrifying bacteria and can kill of good portion of your population over time. It also strips oxygen from the water by binding with it. Depending on the dose rate use the amount of free O2 that gets used up can be substantial.