You can buy a collar for something like $10 that will supposedly deflea/prevent fleas from going near your cat. I remember putting it on my cats (it was a bit bulky) but it did the trick. Ive never had fleas on any of my 3 cats.
As for letting them outdoors, Id suggest it unless your neighbors let their dogs run free. If they are on leashes you should be fine, but watch the cat when its outside until they are about a year or so old.
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