Woman on bus
Q: It is permissible for a man to sit next to a woman on the bus, if there is no other place?
A: Yes. But he should not look at her and be careful not to touch her (Shut Igrot Moshe, Yoreh Deah 2:83. Even Ha-Ezer 2:14. A young man was once sitting next to Rav Shlomo Zalman Auerbach on the bus when a woman got on and there was no place for her to sit. Rav Shlomo Zalman said to the young man: Either you should stand up and allow the woman to sit or I will. The young man stood up and the woman sat next to Rav Shlomo Zalman. Ve-Alehu Lo Yibol vol. 2, p. 182. Although another time Rav Shlomo Zalman was sitting on a bus, and an immodestly dressed woman got on and sat next to him. Instead of continuing to sit, which was unpleasant and a Chilul Hashem to those who saw or standing up and potentially offending her, Rav Shlomo Zalman got off at the next stop and waiting for the next bus. Ha-Torah Ha-Mesamachat, p. 289).
Beginning of Redemption
Q: When will the Redemption finally begin?
A: It began 130 years ago with the building of the Land of Israel and the ingathering of the exiles, and one should not have a lack of gratitude to Hashem, G-d forbid.
Torah and Science
Q: Were the statements of our Rabbis regarding science stated with "Ruach Ha-Kodesh" (Divine intuition) or according to the science of their time?
A: Some and some. For example, the medical instructions in Massechet Gittin are the science of their time, as explained in Otzar Ha-Poskim, but the Laws of Tereifot are oral laws given to Moshe Rabbenu at Mt. Sincai, as explained by the Rambam and Rashba.
Drafting Torah Scholars into Tzahal
Q: If Rabbis do not require protection (Baba Batra 8b), why should those who learn Torah be drafted into Tzahal?
A: See the responsa of the Radvaz (2:752) who gives three answers: 1. This is not said about every Torah scholar. 2. A Torah scholar who requests protection reveals that he does not rely on his merit. 3. This is stated regarding protection in monetary matters and not life-threatening situations (Shut She'eilat Shlomo 1:368).
Picture of Lion
Q: Is there a problem to hang a picture of a lion in a child's room because it is a non-Kosher animal?
A: There is no prohibition to have a picture of a non-Kosher animal or a toy in the form of a non-Kosher animal. By the way, many Ashkenazi shuls have lions on the ark curtain. Be courage like a lion (Igrot Ha-Re'eiyah vol. 1, Igeret #10. Shut Aseh Lecha Rav 8:60. The Lubavitcher Rebbe, however, was strict about this practice. And this is the custom of Chabad Chasidim. Likutei Sichot vol. 25, pp. 309-311).
Q: If someone badly abused me, is it an ethical or halachic problem if I burn his picture?
A: There is no problem. He should be grateful that we don't burn him.
Student who Caused Damage
Q: A student caused damage in the school, but the teacher does not know which student. Is it permissible for the teacher to ask the students to tell him who did it?
A: He should ask the students to bring him the money for the damage within a particular time period. If they wish, they can all pitch in money. If they wish, they can collect the money from the one who caused the damage.