Is it prohibited for a fingernail biter to swallow his nails based on the prohibition of "Bassar Adam" (or any other prohibition)? If not, may one swallow nails on a fast day? Can you please include any sources in your response.

Without going into a discusssion of which prohibition forbids us the eating of human flesh and whether "bassar min hachai" or "yotzei min hatamei" applies to it- there is a prohibition against eating things which are disgusting: "bal teshaktzu". For this reason, consuming human waste is forbidden even if "yotzei min hatamei" does not apply (Shulchan Aruch Yoreh Deah 116 6; Shu"t Radbaz II 739; Shach Yoreh Deah 81 3; Talmudic Encyclopedia "Bal Teshaktzu").