Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
How is night prayer offered?
Night prayer is offering voluntary prayer after Maghrib and before Fajr (Dawn). As for Tahajjud, it is offering voluntary prayer at night after waking up voluntarily, and for Allah`s sake as He Says (What means): "And pray in the small watches of the morning: (it would be) an additional prayer (or spiritual profit) for thee: soon will thy Lord raise thee to a Station of Praise and Glory!" [Al-Isra`/79]. Offering Tahajjud is better than offering voluntary prayer before going to bed.
Is it permissible for the woman to use her mobile phone while on the street?
All Perfect Praise is due to Allah, The Lord of The Worlds
Modesty should be observed by the woman at all times, so she is free to use her phone while on the street as long as it is done within the limits of Islamic manners. And Allah The Almigty Knows Best.
Is it permissible for the person who wants to travel from the United Arab Emirates to Jordan during the daytime in Ramadan to break his fast before leaving his country; knowing that he had embarked on journey half an hour after dawn?
Praise be to Allah the Lord of the Worlds.
The person who made the intention to embark on journey after dawn must observe fast for that day, because it became an obligation on him before engaging on journey. However, if he experienced unbearable hardship while on travel, then he is permitted to break his fast, but he must make up for the missed day. And Allah The Almighty Knows Best.