Yes, removing the cats from the area treated with Precor IGR is a good practice. They can go into an area that has not been treated until the treated area dries completely. This generally takes 1-2 hours depending on how heavily you spray.
Yes, Precor IGR Concentrate can be sprayed on pet sleeping and bedding areas. This is just a growth regulator so it will not kill any fleas. It will simply stop their lifecycle.
Another option is to use Ultracide. It is very effective flea control aerosol that provides immediate kill of adult fleas and prevents formation of new adults from eggs or larvae. Ultracide dries quickly and will eliminate flea problems for up to seven months. This can be used on pet bedding and pet resting areas, as well as various areas where there is a flea infestation. This treatment will be done every 14 days until you no longer see activity. Make sure that you are still vacuuming daily as well.
Yes, if Precor or any insecticide got on any blankets or sheets used for sleeping on you would need to wash them before using them again.