chatzi shiur by kiyum mitzvah; the famous Taz about not legislating against en explicit pasuk; how long did Mordechai live?

1) The Minchas Chinuch in a few places raises the question of whether there is any value to a kiyum mitzvah done with a chatzi shiur. Do you, for example, get any credit for eating half a zayis of matzah, or is it all or nothing? He brings proof from the fact that when they gave out the lechem ha’panim each kohein only got a small piece less than a k’zayis. Even though there is a mitzvah of achilas kodshim, and achila by definition = a k’zayis, apparently eating even less than the shiur had some value. The Beis haLevi rejects this proof and distinguishes between achilas kodshim, where the mitzvah is that the cheftza be consumed, and achilas matzah, where there is a chovas hagavra to eat. However, the Netziv in last week’s parsha (6:22) is so emphatic about the fact that even the mitzvah of achilas kodshim requires eating a k’zayis that he suggests that eating less is close to being a violation of the issur of being ne’heneh from hekdesh. He is forced to concede (based on the proof from lechem ha’panim) that it’s not a real issur, but it’s certainly not something you want to avoid.

2) Chazal (Brachos 2) made a seyag that even where m’doraysa a mitzvah can be done all night, it should be completed before chatzos. The Rambam applies this din to all the cases mentioned in that Mishna, but Rashi writes that it applies only to kri’as shema but not the burning of the fats and meat of korbanos on the mizbeiach. My son alerted me to the Torah Temimah (6:2 comment #7) who explains Rashi based on the Taz’s famous principle (Y.D. 117) that the Chachamim can never uproot or change a din written explicitly in the Torah. Since our parsha says explicitly that korbanos can be burned “kol ha’layla ad ha’boker,” all night, the Chachamim could not limit the time in any way. (The L. Rebbe suggested that even the Rambam may accept the Taz’s principle, but only with respect to curtailing the performance of an actual mitzvah. In our case, there is no mitzvah to davka burn the fats at night – it is just permissible to do so if it was not done during the day.)

3) For those who are still holding by Purim, an interesting Rashi in Menachos 64b: the gemara there relates that during the Hasmonean wars, there was an attempt to disrupt the avodah.  All the wheat and barley around Yerushalayim was burnt so that the korban ha'omer and shtei halechem could not be brought (Maharasha).  There was a mute person who tried to signal where wheat could be found, and the gemara says it was Mordechai who understood the hint and figured out the name of the places based on the gestures.   Rashi there comments that this is the same Mordechai from the Purim story.  If so, it would mean Mordechai lived an amazingly long life!  Tosfos therefore rejects this view.  I don't know if anyone has a hesber for Rashi -- seems to be an argument about metziyus.