Does Husband fasting while being impure for having sexual intercourse with his wife at night permissible?
Yes it is permissible for you to fast because impurity isn't among valid fasting conditions, but you are obliged to perform ritual impurity in order to catch up Fajr prayer at its due time. And Allah Knows Best.
Is Hyena's Meat Permissible or Impermissible?
All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
There is disagreement amongst the jurists as regards the ruling on eating hyena`s meat. Shafi`i and Hanabli jurists are of the view that eating hyena`s meat is permissible. The proof is the Hadith related by Al-Baihaqhi on the authority of Ibn Abi Ammar who said: "I asked Jabir bin Abdulla about hyenas, and he told me to eat them. I said: "Is it not game? He said: 'Yes' I said: 'Did you hear that from the Messenger of Allah?" He said: "Yes." And Allah The Almighty Knows Best.
Is it obligatory for a wife who has been abandoned for many years to observe the waiting period (iddah) after her husband passes away?
If her husband passes away, the wife is required to observe the waiting period (Iddah), even if he had abandoned her, because she is his wife and inherits from him, so she must observe the iddah after his death. And Allah Knows Best.
Is it permissible for someone who has forgotten to mention the supplication pertaining to answering the call of nature to say it while in the toilet?
It is disliked for a Muslim to mention Allah while in the toilet, but he/she may recall the supplication in his/her head without uttering it; that is in case he/she had forgotten mentioning it before entering the toilet.