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.
What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.
What is the ruling on looking at pictures of naked women via the internet?
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.
It is impermissible to look at pictures of naked women via the internet, and this act is forbidden according to Sharia. The proof of this is that Almighty Allah Says (What means): "Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: And God is well acquainted with all that they do." [An-Nur/30]. Therefore, we advise you to busy yourself with offering acts of obedience that draw you closer to Allah and prepare yourself for meeting Him on The Day of Judgment. And Allah The Almighty Knows Best.
Is it permissible to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?
It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.