No, there is no need to clean carpets, furniture or other surfaces after fogging (although doing so will not impede the peformance of the product). Items that your kids might put in their mouths, such as toys, should be removed before fogging.
If you fog and ventilate as directed on the packaging, you can reuse the treated area (and items in the treated area) as you would normally. If you would feel more comfortable, you could always cover your mattress and keep your drawers closed during treatment if those aren't problem areas. Washing your bedding after treatment won't affect the performance of the product, either.
Will this product kill Brown Recluse and Black Widows?
I have a detached garage that we are about to demolish. It is infested with spiders of all sorts; namely black widows and brown recluse. Before we get started with tearing it down, we want to get rid of as many spiders as possible, in hopes that they don't find home in our home! Will it work to kill them? It is approximately 200 sq feet, how many cans should I use?