Talstar P (Talstar One) after dilution is only strong enough to kill small insects. Your puppy would have to eat loads of treated grass for Talstar it to harm it. Be sure to keep the puppy out of the treated area until dried.
Use a 0.06% dilution of Talstar P (1 fluid oz. per gallon of water) for bedbug control. A thorough application should be made to crack and crevices where evidence of bed bugs occurs. This includes bed frames, box springs, inside empty dressers and clothes closets and carpet edges,high and low wall moldings and wallpaper edges. Do not use this product on bed linens, pillows, mattresses or clothes. Remove all clothes and other articles from dressers or clothes closets before application. Allow all treated areas to thoroughly dry before use. Not recommended for use as sole protection against bedbugs. If evidence of bedbugs is found in/on mattresses, use products approved for this use such as Bedlam aerosol and Protect-A-Bed mattress, boxspring and pillow encasements
While we do not recommend to apply Talstar P (Talstar One) at a higher rate than 1oz, your lawn should be just fine. Please keep in mind that it's also recommended to apply during cooler times of the day.
Yes, Talstar P will be a great choice for treating listed areas for Japanese Beetles. You will mix 1 oz per gallon per 1,000 sq ft.
It should not harm anything to apply Talstar at this rate one time. We recommend that you wait for 30 days outside (90 days inside) to reapply at the rate of 0.5-1 oz per gallon of water.