ANSWER: If this hair is coming in the eye, causing nuisance or blocking your view then no problem in cutting it short due to necessity. However, you must not touch any other hair at all. 

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ANSWER: Yes, lower your gaze and listen to the lecture without seeing her.  https://www.assimalhakeem.net/are-boys-allowed-to-study-at-mixed-universities-knowing-that-in-our-country-all-universities-are-mixed-2/

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ANSWER: No problem at all in giving money in an envelope or gifts on such occasions.  Giving gifts is part of the Sunnah. However, forcing people to give or be slandered like this, this is totally prohibited and the whole community is sinful for not changing this bad habit which burdens the poor. 

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