We would not recommend spraying either Temprid nor Dragnet SFR inside the cage itself. You should thoroughly clean and wash the cage instead. Then treat the rooms the cages are kept in, removing the rats completely during treatment and until dry.
We would recommend using one of our roach control kits to treat.
We also have a great article with more information on roach control.
Dragnet SFR (which has been discontinued by the manufacturer a while back) does list carpenter ants on the label but it only refers to the control of root weevils and not all weevils in general. If you have this product already and are looking to spray it around the foundation of the home the ingredient in it will likely kill most any insect that crawls over the treated surface. If you are having trouble with carpenter ants indoors you would typically want to bait for them to eliminate the whole colony. For grain weevils, clean out any infested materials in the home and use a general insecticide like Suspend SC for cracks and crevices if treating a large area, or if small areas like cabinets and pantries use an aerosol product like Cy Kick or D-Force.
Carpenter Ant Control Guide
The comparable product listed on the Dragnet SFR product page is Permethrin SFR 36.8%. Yes, Permethrin SFR 36.8% is labeled to control carpenter ants. We also suggest you check out our Carpenter Ant Control Article to achieve the most effective results. The treatment article will also offer helpful information for eradication and prevention.
Dragnet SFR is rainfast 24 hours after the application has dried.