the best way to check for fleas is their poop. And so easy too for kittens:
grab the cat, put a piece of white paper on table or floor under the cat, and now ruffle up his fur as if you wanted to make dandruff fall off. There may be sand and other dirt things on an outside cat BUT flea poop is dried blood, so put some drops of water on the paper, and let the water slide off a bit, if you get tiny red streaks, it's flea poo for sure!
For the house, there's loads of different products, my parents always used the "bombs" where you have to take the animals out of the house, put the bombs and leave the house for 3h and then aerate. the bombs put a flea killing product everywhere that also kills the eggs i think.