Can I start fasting based on the moon sighting of another country?
You must follow the moon sighting of the country you are in.
In the Sharia-compliant viewing at a prospective bride (*al-naẓrah al-sharʿiyyah*), is it permissible for the man to see the woman without a veil (*ḥijāb*)?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
It is sunnah for the suitor to see the woman he is seeking to marry within the limits the Sharīʿah permits, namely looking at the face and the hands (palms and backs), based on the saying of the Prophet (peace and blessings be upon him): “Look at her, for it is more likely to bring about harmony between you.” Narrated by al-Tirmidhī.
The suitor may also ask one of the women to look at the woman he is seeking to marry. In that case, she is permitted to see of her what she is normally permitted to see, which is not limited to the face and hands, and she then describes these matters to the suitor. It is narrated on the authority of Anas (may Allah be pleased with him) that the Prophet (peace and blessings be upon him) sent Umm Sulaym to look at a girl, and said: “Smell her breath, and look at her heels.” Narrated by Aḥmad in his Musnad.
It is stated in Tuḥfat al-Muḥtāj (Vol.7/p.192): “For one who cannot easily look, or does not wish to look himself, it is sunnah to send someone who is permitted to look at her, to observe her and describe her to him, even regarding what he himself is not permitted to look at. He thereby gains through the sending what he would not gain through looking. Because of the added need for this, it is excepted from the prohibition of a woman describing another woman to a man.”
The permissibility of looking is conditional upon his resolve to marry her once he is able to, his predominant assumption that his proposal will be accepted, and his assumption that the woman is free of marriage and of a waiting period (ʿiddah). Otherwise, looking is forbidden.
Accordingly, it is not permissible for the suitor to look at anything other than the face and hands. He may ask one of his maḥram women, such as his mother or sister, to see the woman unveiled, and the Sharia-compliant viewing (of a prospective bride) must take place in the presence of one of the woman’s maḥrams. And Allah Almighty knows best.
Is it valid to share in the 'aqīqah by contributing a seventh share of a camel or cow?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
Yes, it is permissible. If a group of people jointly share in the slaughter of a camel or a cow on behalf of seven individuals, this is valid — regardless of whether all of them intend the 'aqīqah, or some intend the 'aqīqah, others the uḍḥiyyah, and others simply the purchase of meat. And Allah Almighty knows best.
What is the ruling if hemorrhoid blood exits after completing ablution?
If this blood is exiting from outside the anus (due to the hemorrhoid protruding), it does not invalidate ablution, because blood exiting from the body from other than the two orifices does not invalidate ablution. If it exits from the anus (meaning from inside it), it invalidates ablution, and one must perform istinja' from it, wash the area of impurity, and repeat the ablution.
However, if this blood exits continuously such that no time remains sufficient for purification and prayer without it flowing, then it takes the ruling of urinary incontinence (sals al-bawl). One then cleanses from it after the time for each prayer enters, performs ablution immediately thereafter, and performs the obligatory prayer immediately. There is no liability upon him after that if something of it flows, and he may pray as many voluntary prayers as he wishes. If he wants to pray another obligatory prayer, he must cleanse himself and perform ablution. And Allah the Almighty knows best.