Health: Source for #1 please. Also, See Sukkah 9b or 10b (I think) which seems to prove you wrong on that K’lal. Tzitzis is also a Mitzvas Asei Shehazman G’rama according to what we hold.
#2: See the Rama in 38:3 and the Nos’ei Keilim there and it’s unclear what the reason is. (I should have said Rama, not SH”A.) I have a long Shittah on that which I don’t feel like typing out here at the moment.
#3: That Kaf Hachayim is not the majority Shittah in the Poskim, though it is far from a small minority. There is good reason to say that it doesn’t apply to a Tallis Kattan though. Mentioning that was one of the reasons that I convinced her to tuck them in with.
Rav Ovadia and the Tzitz Eliezer both have T’shuvos about a single woman wearing a Kippah for Davening. R’ Ovadia’s answer might surprise you. But yes, most women who were Kippas aren’t really doing it to be Shomer Halacha and probably don’t care.