Yes, Bifen IT can be used in a hose end sprayer. You will use 1 fl. oz. of solution and 5.5 ml of Nyguard IGR per gallon of water. You will put the concentrate directly into the cannister, and the tube will automatically use how much you have on the dial. It will disperse with each gallon that comes through the hose. You will need to be as accurate as possible when using this method. Please let us know if you have any additional questions.
Bifen IT is an excellent insecticide and is labeled for ants, including fire ants.
Vector Ban Plus does not leave any kind of residual so will only kill the mosquitoes that are out in the open at the time you are applying to product.
You are on the right track with using a residual product like Bifen IT or Demon Max, it is actually our most popular product for mosquitoes. The key is to apply it to the underside of leaves of trees and bushes as that is where the adults lay during the day. Bifen would be the more recommended as it known to be super gentle on plants but you can rotate them as well.
When doing a soil barrier treatment for termites, it is important to treat directly against the structure on all sides of the house as close as possible. Against the foundation of the home, dig a 6 x 6 trench around the entire perimeter. Where carports and concrete patios are existing, you will drill 18-24 inch holes 2-3 inches off the foundation wall 10-12 inches apart. This will ensure the soil under that concrete slab is protecting the actual house foundation. Please read our on How To Perform A Termite Treatment Article for more detailed instructions and recommendations.
While Bifen IT is labeled for termites and will last up to 5 years in the soil, we would recommend using Termidor SC or Dominion 2L for termite soil barrier treatments. Termidor SC bonds to the soil after 24 hours and will last 10 years and Dominion 2L will last for 7 years.
We are not sure what type of worm would be considered a "red worm" as you have described.  If you are referring to earthworms, Bifen IT is not labeled for earthworms, because they are a beneficial but it may cause harm to them if they contact a treated area.  Though they are pretty protected by the mucus on their bodies. This small amount of product needed to kill tiny insects would not be enough to harm a bird if they were to ingest a worm that would have contacted the product.
We do sell professional Roach Bait Gel and Ant Bait Gel. Follow the links to which ever one you are inquiring about. We also carry bait granules and insecticide granules for pest control. Please read the labels for specific instructions on application.