Talstar P should be used or discarded within 24 hours of mixing.
Talstar P is not labeled for use to control root aphids or for use in a vegetable garden. Pyganic Gardening or Azera Gardening can be used in and around vegetable gardens for aphids and a wide variety of other insects. Keep in mind that this is a persistant pest often brought into an area by infested plants or soils, so be sure that you are checking transpants and using clean soils in your garden.
No, Talstar P is an insecticide that does a great job killing insects, but it will not kill mice.
Talstar P would be best applied in the early morning or late evening and not during the heat of the day to prevent burning on the grass.
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.