2. A few years ago we mentioned (I, II) R' Akiva Eiger and the Turei Even's sevara that although bikkuim are brought only between Shavuos and Chanukah, the mitzvah is not classified as an aseh she'ha'zman gerama because that's simply the time period when the cheftza shel mitzvah of fruit is available -- it's not a limitation on the duration of the chiyuv. (This is similar to R' Chaim Brisker's explanation as to why milah is not categorized as zman gerama [see Tos. Kid 29a] -- the baby is simply not a proper cheftza shel mitzvah until day 8, but there is no time limitations on the chovas hagavra.)
It seems that the MG"A takes a different view, as he (O.C. 424) quotes the SHL"H that women are exempt from kiddush levana because it is a zman gerama mitzvah. R' Shlomo Kluger asks: Why is kiddush levana any different than bikkurim? There is no limitation on the chiyuv -- it's just that the cheftza shel mitzvah, the new moon, is available only certain times during the month. It's a metziyus, not a din.
I know it's a dochak, but this is only a blog, so I'll try out a chiluk. R' Elchanan in the Koveitz Shiurim at the beginning of Pesachim has a chakirah whether the emergence of three stars is a siman that it is night, or the emergence of stars is the sibah of it being halachic night. I want to go a step further and say that when the Torah tells us that the passage of the sun and moon and stars are "l'yamim v'shanim," it means not only are they the means of marking time, but they are the sibah for time changing. Bikkurim are a phenomenon that takes place within the envelope of time; the passage of the moon is the phenomenon of time, and is therefore directly related to zman.
Parenthetically, the Halichos Beisa quotes a beautiful kashe in the same of R' Isser Zalman Meltzer -- whether it's zman gerama or not, why are we referring to kiddush levana as a "mitzvah"? There is no mitzvah to go out and find the moon -- there is just a din that if you see the new moon, you are obligated to say a birchas ha'shevach. See his answer (end of ch 16) in the name of the Chazon Ish.