Is it permissible for a religious young Muslim woman to love a young man for Allah`s sakes?
Such love between the two sexes is from the devil`s evil suggestions, and a pure Muslim woman should beware of such a matter, and she shouldn`t mix with non-Mahrams(Marriageable ).
Is it permissible to shorten the eyebrows if they get too long?
Yes, it is permissible, but not desirable.
If the Prophet (PBUH) was an Arab citizen in 2009, born in an Arab country ruled by an Arab ruler, saw what was happening to Gaza, what would he (PBUH) have done?
All perfect praise be to Allah, The Lord of The Worlds. May His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
Had the Prophet (PBUH) been amongst us, Muslims would have supported him, and then he would do whatever pleases the heart of every Muslim. And Allah The Almighty Knows Best.
Is a woman`s nephew by suckling considered a Mahram( i.e. unmarriageable)who is permitted to accompany her to Hajj?
All that is prohibited by lineage is prohibited by suckling, and a nephew by suckling is a Mahram like a nephew by lineage ;therefore, it is permissible for him to be a Mahram for his aunt in Hajj and Umrah.