Can Zakah or Zakat al-Fitr be given to a poor brother?
Yes, it is allowed to give Zakah or Zakat al-Fitr to a poor brother, as he is considered among the eligible recipients.
Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?
It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.
Is it permissible to offer an absentee funeral prayer?
Yes, it is permissible to offer an absentee funeral prayer.
A man insulted the Divine Essence; is it obligatory for him to perform Ghusl?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Insulting or blaspheming the Divine Essence (Dhat al-Ilahiyyah) constitutes apostasy (Riddah). The perpetrator of this grave sin must immediately repeat the two testimonies of faith (Shahadah) and sincerely repent to Allah the Exalted. It is recommended (Sunnah) for them to perform a ritual bath (Ghusl), though it is not a mandatory condition [for the validity of their return to Islam]. And Allah the Exalted knows best.