D.S.
I hate legos. So I'm no help there. But I'd definitely try to restrict them to one room.
But I've had cats and dealt with cat hair since I can remember. I have been catless for about 3 yrs. Catless is way better.
Cat's have different kinds of hair. My Maine Coon didn't shed a lot. My rag doll shed like you wouldn't believe. I brushed her routinely out doors and enough hair came off to make another cat. And still there was hair left to brush. I think it grew back as fast as I brushed. It blew through the neighborhood like cottonwood seeds. It was a sight to behold. It piled at the corners of the fence in my back yard like a small snow bank. In the house it wafted across the kitchen floor like cotton wool.
My daughter has a cat with short spikey needle hair that gets on everything and won't be vacuumed.
So the bottom line is you have a cat. You have cat hair. Deal with it. Sorry.
I changed my last cat's name to Elsie. (LC. Last Cat.) Swiffers. Lots of Swiffers.