Can Fleas lay eggs if they've not bit the Cat?

Our Cat had Fleas so we gave him Flea Tablets and Spot On treatment and Sprayed the house with a Flea Spray it appeared to work but over the past couple days Fleas have been appearing again even though we are hoovering daily. We were wondering if once the Cat has had his treatment if any Fleas that bite him can still lay eggs? Also should we keep the Cat in one room or let him into others or will this just allow the Fleas to bite him and lay more eggs? Any tips on how to kill the buggers would also be much appreciated, thanks.