What is the ruling of killing an animal for no reason? Which animals are eligible for sacrifice in EID, and can someone sacrifice animals for the sake of Allah on any other day? Please give evidence.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Animals, birds, ants are all among the creatures of Allah who worship Allah and Glorify Him.  Allah Says (interpretation of meaning): {The seven heavens and the earth and all that is therein, glorify Him and there is not a thing but glorifies His Praise. But you understand not their glorification…..}[17:44].

So, killing them is not allowed except those which attack human beings or harm them like the five animals that are mentioned in a Hadith that the Prophet (Sallallahu Alaihi wa Sallam) said: "It is not sinful to kill five kinds of animals, namely: the crow, the kite, the mouse, the scorpion and the rabid dog."

Also slaughtering lawful animals to eat their meat is permissible.  But killing without any legal reason or killing those animals the Shariah prohibits killing such as killing ants, shrikes, frogs, etc. is unlawful.

Imams al-Shafi’e, Ahmad, Al Nasa’e, and Ibn Hibban narrated from Amar Ibn al-Shareed that he said, I heard the Prophet (Sallallahu Alaihi wa Sallam) saying whoever kills a sparrow uselessly, it will raise its sound complaining against him the Day of Judgment, O Lord, so and so killed me uselessly and did not kill me for any benefit”. 

Imam al-Shafi’e and al-Hakim narrated in a Hadith which al-Hakim considered Saheeh that the Prophet (Sallallahu Alaihi wa Sallam) said: "If a person kills a sparrow or less than a sparrow without right, Allah will question him about it.  They asked him, “What is the right O Messenger of Allah? He answered, “Slaughter it and eat it, do not cut its head and throw it”.  As for killing animals without any legal reason or considerable benefit, it is not permissible."

As for animals that are sacrificed during the Eid of Al-Adha (Uduhiyah) they are camels, cows, sheep and goats.  Any kind of animals other than what is mentioned here is not sufficient in Uduhiyah or in Hadi.  The time of Uduhiyah is the Day of Eid al-Adha and three days after it.  If one slaughters after that time it is not considered as Uduhiyah. If a person slaughters after that time with the intention of Sadaqah (charity) or to feed his family members he will get its reward.  Likewise, one is rewarded if he slaughters after his Umrah or perform Aqiqah.  It is also permissible to slaughter any animal that is lawful in Shariah and to give it as alms, Allah will reward that.