My cat has worms

[khawk]

I have a 13 y/o cat, a 6 y/o cat and a 9 y/o dog (a pug). I noticed what appeared to be worms in my oldest cats feces. They were small and white, about the size of grain of rice. I did some searching online and it seems to be what I think might be a piece of tapeworm or an egg from a tapeworm. Both my cats are strickly indoor cats and never go outside, my dog goes outside but doesnt stay out long, he is on a run and doesnt run loose. Im calling the Veterinarian tomorrow morning to see about getting my oldest cat in there and I have a sample of her feces. Im guessing if she is infected so are my other 2 pets. I inspected my dogs feces and dont see any worms but about a month ago he was sitting on the floor and going around in a circle like he was scratching his butt. someone told me thats a sign of worms but Ive never seen any around his anus or in his feces. Im very concerned about my 4 legged kids. Im also concerned about the worms being around the house, my pets sleep in my bed with me, lie on the furniture and on my kids beds. Do the worms die once they are outside of the animals body? I cant figure out how my pets got these worms. I did read something about them eating fleas but I havent seen a flea on any of my pets in about 7 yrs. Does anyone know anything about these worms? Are they easy to get rid of? Can they harm my pets? Can me or my kids get them? None of my pets seem to be losing weight. Thank you.
Khawk