Is a wife considered divorced if her husband refused to go to bed with her (for sexual intercourse) for two months?
A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.
Is the prayer of someone who didn`t face Quibla (Ka`ba direction) valid?
All perfect praise be to Allah,The Lord of The Worlds. Facing the Quibla is a condition for the validity of prayer, and the prayer of the person who hadn`t faced the direction of the Quibla is invalid, and he is obliged to repeat it. And Allah Knows Best.
Is ablution invalidated when blood comes out of the nose, or a wound?
Blood coming out of the nose, or a wound does not invalidate ablution, but it is preferable to make ablution as a way out of the scholars disagreement in this regard.
Is it permissible to make ablution without answering the call of nature after waking up?
Washing front and back openings (Istinjaa`) is not a condition for the validity of ablution because it is done to remove Najaasah (impurity), thus if there is no Najaasah, there is no need for that, and then it is permissible to make ablution without answering the call of nature. However, prayer is invalidated if there is Najaasah on the anus ,or the front opening, so it (Najaasah) must be removed for the prayer to become valid, and not the ablution.