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.
Talstar P (Talstar One) should NOT be applied to lemon trees or other edible vegetation. If the edibles were treated, you should not consume the fruit. Please provide the targeted pest for an alternate product recommendation for treatment.