Talstar p is labeled for bedbugs but according to the product label it should not be the only product that you use for bedbug control. Most folks purchase and use our bedbug kits for bedbug control as they come with all of the products that will be needed. You can see our bedbug kits by following this link: BEDBUG KITS.
http://www.domyownpestcontrol.com/bed-bug-kits-c-39_97.html
Talstar P is not labeled for nor recommended for bird mites. Onslaught Insecticide would be a better option and is labeled for mites in general.
Yes, Talstar P (Talstar One) is labeled for gnats and roaches. You will use 1 fl. oz. per gallon of water. This can be sprayed around the perimeter of your home, on trees, bushes, broadcast across your lawn, etc. It cannot be sprayed on any type of edibles or area where animals would graze.
We would also recommend mixing the Talstar P (Talstar One) with Gentrol IGR. This will stop the roaches from reproducing for up to four months.