Yeah it could have been throup (ew)
or a Hair Ball (every cat has them )
I think its probably a Hair ball cause it kinda sounds like my cats hair balls (yuck .lol.)
Yes ithink it is normal i think she is cousise(how do ya spell that again lol i forgot) but...and i my cat digs at the carpet but she does that for her nails maybe to sharpen or to make them shorter i have noclue but she only has baq(back) claws so..its kinda funny.
I hope you find yourt lil one soon.! Thats very sad , but maybe she is exsploring outside or if in side she might be in a closet or something ...cause my friend couldnt find her cat but we found her in one of her dark closets...((but with kittens!!)) any way i really do hope you find her...