In fact, the use of red food coloring in your solution is both unnecessary and unhealthy for the birds, especially when your feeder already has the appropriate red plastic blossom. Never use honey when making your own nectar mix. Honey will attract bees as well as a black fungus that will cause a fatal liver and tongue disease in hummingbirds. In addition, don't be compulsive about removing small insects found in the mouth of the feeder. They fulfill the protein requirements for hummingbirds and should not be removed from the feeder until cleaning.
Hummingbird feeders require cleaning every two to three days, especially in warm weather.
Feeders should be washed with a solution of one tablespoon white vinegar and one cup water. Use a bottle brush to clean hardened debris on feeders, and rinse thoroughly with warm water. Yes, it will hurt the tree and is not what I would recommend to control the borers. Anything that penetrates the bark of the tree injures the tree permanently. Nails, wire or other material tied around a tree trunk, and even pruning are harmful to the tree.