A] The צר המנבח can be the yetzer hara [Rav Shlomo Fischer Shlita] or Amalek [many others - sources are marshaled for both assertions]. After they are discarded אז אגמור בשיר מזמור חנוכת המזבח - the third beis hamikdash will be rebuilt.
B] The Sha'arei Teshuva (673:12) cites a ruling from the Shevut Yaakov (3:48) whereby this halakha has application even in cases of a house with but a single entranceway. The Shulchan Arukh (O.C. 673:2) rules that if one's Chanukah candles were extinguished before they had burned for the minimum required duration, one is not required to rekindle them (provided that they had initially been lit with enough oil or wax to burn for the minimum duration). The Shevut Yaakov claims that while one need not rekindle the candles in such a case, he must leave the candles near the entranceway until the minimum required period has passed, so as to avoid suspicion. In his view, just as the Sages required lighting candles in all entranceways to avoid suspicion, so did they require leaving the remnants of one's candles after they have been extinguished, lest pedestrians mistakenly conclude that the individual has neglected the mitzva.
Rav Shlomo Zalman Auerbach (as cited in Halikhot Shelomo) disputed this ruling of the Shevut Yaakov. He understood this requirement to light at a second entranceway as applying only at the time of lighting itself. The obligation of Chanukah candles requires pirsumei nisa, publicizing the miracle, and for this reason one must light in a manner that achieves the greatest publicity and avoids any possible impression that candles were not kindled. Chazal required lighting in the second entrance as part of the obligation of pirsumei nisa, which applies only at the time of lighting, and not thereafter. Hence, one is not bound by this halakha once he had already lit the candles, even if they were prematurely extinguished.
Rav Shlomo Zalman suggesting applying this theory concerning the requirement to light by the second entrance to resolve a difficulty raised by the Beit Yosef (O.C. 671:8). The Gemara in Masekhet Berakhot (8a, 61b) establishes that one should not pass in front of an entrance to a synagogue during services without stepping inside, as this gives the appearance of disinterest in participating in the service. If, however, the synagogue has several entrances, one may pass by an entrance, as people will grant him the benefit of the doubt and assume that he will be entering through a different entrance. Why, the Beit Yosef asks, do we not apply the same rationale in the context of Chanukah candles? Why do we not trust that people will assume the individual has lit Chanukah candles by the second entrance?
Apparently, the halakha concerning Chanukah candles differs because of the interest in achieving maximum pirsumei nisa. Even though most people would give the benefit of the doubt, as we assume in the case of walking past a synagogue, the prospect of some pedestrians entertaining fleeting suspicions regarding the individual's candle lighting suffices to mandate lighting in the second entrance. Since this requirement stems from the strict demands of pirsumei nisa, we are more rigorous in insisting upon avoiding misperceptions than in other similar contexts, such as passing by a synagogue during prayers.
