Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
What is the ruling on loudly sending prayers on the Prophet (PBUH ) after the call for prayer Athaan?
All perfect praise be to Allah, The Lord of The Worlds Sending prayers on the Prophet after Athaan is a Sunnah for the Mou`zen (caller for prayer ) and the hearer. However, there is no harm in doing it loudly after the end of Athaan, but sometimes, it shouldn`t so that people wouldn`t think that it is an integral part of the Athaan. And Allah Knows Best.
Is it permissible to offer Tahajjud prayer after Witr prayer?
It is permissible to offer voluntary prayer after Witr (An odd number prayer performed between Isha and Fajr) prayer. However, it is desirable that the night prayer be ended with Witr. Therefore, it is desirable for one, who thought that he was most probably going to wake up at night in order to offer Tahajjud, to offer Witr after it, but one, who fears that he might not wake up, should offer Witr before going to bed.
have an amount of 2,700 Jordanian dinars, which I have invested in a project, and I pay zakat on it every year. However, I have debts and obligations, and this project yields only a profit of about 2-4%. My salary is not enough to support myself and my family to the extent that I cannot pay the electricity bills. Is it permissible for me to take from the above Zakat?
You permitted to take from your Zakat since your income insufficient for you, because the poor is permitted to take from the Zakat in general, besides; the poor is identified of whose income doesn't suffice him. And Allah Knows Best.