Have you tried flushable litter? I got the litter box a few years ago that had 3 layers to it that you could sift. The waste fit into a walmart bag and easy to dump into. It worked great and it was around $20. I also keep a rubber mat under my litter box to catch the overflow.
As far as getting hair up, there is a new carpet fresh out that has "Pet Release" in it. Haven't tried it yet. I find a shop vac works the best for picking up hairs. I also got a small steam cleaner for accidents. There is a "sponge" for about $3 that works great for pet hair. You can find it at a pet store or walmart. Brewer's yeast is also good for preventing alot of shedding, fleas, and gives a shiny coat. Good luck