(a) One is not considered a Rasha for doing an Aveirah b'Shogeg, and therefore he is believed when he says that he killed her husband b'Shogeg, and she may then get married to someone else.

(b) In the case of a Get that is brought from Chutz la'Aretz, we rely on the Shali'ach and we do not have to research it any further. But when a person says that the woman's husband died, even though Beis Din relies on him, as you wrote, nevertheless we must research the witness (that is, the woman checks whether he is saying the truth, and therefore the Gemara says that it "we do not rely on him," because more research is done and we do not rely solely on his words).

(c) That is correct. A Rasha is Pasul l'Edus, even when he is about to die and stands to gain nothing from his Edus. This is a Gezeiras ha'Kasuv.

(d) According to the opinion that requires Mi'un to be done in front of a Beis Din of three, the case in the Tosefta is when she does Mi'un in front of three. According to the opinion that Mi'un is done in front of two, the case in the Tosefta is when she does Mi'un in front of two. However, according to both opinions, there is no need for Mumchin (according to Beis Hillel), as the Tosefta there states clearly, and as the Gemara says later (107b). That is what the Tosefta is teaching when it says that the girl expressed her desire for Mi'un to a storeowner (and there were two or three other men there, as is the normal case in a store).

(e) "Ragil" is from the infinitive verb, "l'Hargil," which means to bring about the thing under discussion (in this case, the quarrel). Rashi is not defining "Ragil" as meaning to quarrel, but rather he is explaining what the person brought about -- a quarrel.

Mordecai Kornfeld