What is the ruling on training dogs that are of benefit?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This is permissible because Allah The Almighty Says (What means): "They ask thee what is lawful to them (as food). Say: lawful unto you are (all) things good and pure: and what ye have taught your trained hunting animals (to catch) in the manner directed to you by Allah. eat what they catch for you, but pronounce the name of Allah over it: and fear Allah. for Allah is swift in taking account." [Al-Ma`idah/4]. However, it is prohibited to keep dogs for no benefit because Salim reported on the authority of his father that Allah's Apostle (PBUH) said: "He who kept a dog other than one meant for hunting or for watching the herd, lost two qirat of his reward every day." [Moslim]. And Allah The Almighty Knows Best.
Is the marriage, which lacks a valid legal contract, a guardian, and a court registration, valid?
It is incumbent that a valid marriage contract be concluded in the presence of a guardian and two trustful witnesses, and it should be registered in the court to protect the rights of the wife. Actually, a valid marriage contract is what differentiates between sound marriage and fornication.
What is the ruling on a person who broke the fast a day in Ramadan due to hardship?
He/she is obliged to make up that day.
Is it permissible for one to masturbate in order not to commit fornication?
This is called committing the milder of the two evils such as eating a carcass in fear of death, and this happens when committing fornication is very likely to occur.