Did Imam Ahmad ibn Hanbal and Ibn Abbas permit masturbation out of necessity, and does that contradict the Qur’an and Sunnah?

The issue is not about violating the Sunnah (definition), but rather it is an ijtihad (definition) (independent reasoning) to ascertain the ruling of Islamic law, and the mujtahid (one who performs ijtihad) is rewarded. As for masturbation out of fear of falling into zina (fornication/adultery), a group of scholars permitted it, while others prohibited it. The jurists held that the intensification of desire is not what is meant by "fear of zina" unless it becomes overwhelming and there are strong inclinations towards zina. The Lawgiver (Allah) has made fasting an alternative to marriage to calm desire.