Your photos of the white specimens are a tapeworm & eggs.
Has your outdoor cat been inside? If not, you may have brought them inside on your shoes or clothing.
Suggest you deworm the cat pronto. If you accidentally ingest a flea, you can become infected with Cat/Dog Tapeworm (Dipylidium caninum).
Cheers - ICU
My Parasite Drug Treatment Protocols: http://curezone.com/forums/fm.asp?i=2012403
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