Talstar P Professional Insecticide is safe for pets if used as directed on the manufacturer's product label. Both people and pets should be removed from the area while the product is being applied, and once the treated area has completely dried, people and pets can re-enter the treated area.
Yes, that will be fine. Everyone will need to be out of the area while Talstar is being applied, but it will be safe for them to return as soon as everything is dry (usually 1-2 hours).
Talstar P would be a great option for indoor spraying along baseboards and in cracks and crevices for general pests.
Talstar P (Talstar One) is labeled to be applied to cracks and crevices indoors. Mopping should not be an issue, as Talstar is not labeled to be applied as a broadcast over the floor. If you were to mop along the edges of the wall where Talstar was applied, it would take it up.
We recommend you use Talstar P. Talstar P should be applied every 30 days at the 1fl oz per gallon of water usage rate from August through to the first frost. If you need to spray high areas you may need to use something like the Chapin Slide Pump Sprayer 6002. This sprayer is much different than most sprayers but there is a video located on the page we have linked for you that will show you how to use the sprayer.