BG 18.17 - The one without the feeling of "I am doer", whose intellect is not tainted, despite killing [others] in this world, neither kills nor is bound
"Is killing justified in the Bhagwad Gita?"
Bhagawad Gita has no firm stand or message on any particular subject. It's more of a description about removing dualities from one's consciousness and fixing it unto the supreme self, which it refers as Atma or ParamAtma. According to Gita, Atma or "self", which is unborn & omnipresent, neither gets killed nor kills. Whatever is happening around the universe is merely interactions of 3 modes (guna-s: sattva, rajas, tamas).
BG 2.21 - Which is said to be indestructible, eternal; One who is unborn, indivisible; O PArtha, how that consciousness (purusha = consciousness = Atma, here) be killed by someone or kill someone?
After all the peace treaties failed between PAndava-s and Kaurava-s, the war was inevitable. Arjuna got confused just during the wartime, which is not a Swadharma or a natural trait for a Kshatriya (Patriot or Warrior). Even if Arjuna had ducked that war, he would have eventually been dragged into it due to his nature.
BG 18.59 - If sheltered by ego, should you think as "Won't fight"; that will be a worthless determination. [Because] Your nature engages you [in fight].
BG 18.60 - O son of Kunti, bound by activities born out of your own nature, you [will] do, which you don't desire [to do] due to illusion.
Also, there is a difference between Killing & Violence.
"Isn't killing (be it human or animal) against the basic tenets of Hinduism?"
Withing the scope of Prakruti, rightful killing is always recommended. Wrongful killing is equally sinful. There are many examples from MahAbhArata. One of them is from Bhishma in RajadharmAnusasana(ShAnti) Parva:
Even a person that is disrespectable, that is of uncleansed soul, and that is very cruel, may succeed in earning great merit as the hunter Valaka by slaying the blind beast (that threatened to destroy all creatures). ......... A deceitful person, falling away from all duties and abandoning those of his own order, always wishes to betake himself to the practices of Asuras for supporting life. Such a sinful wretch living by deceit should be slain by every means. Such sinful men think that there is nothing in this world higher than wealth. Such men should never be tolerated. No one should eat with them. They should be regarded to have fallen down in consequence of their sins. Indeed, fallen away from the condition of humanity and shut out from the grace of the gods, they are even like evil genii. Without sacrifices and without penances as they are, forbear from their companionship. If their wealth be lost, they commit even suicide which is exceedingly pitiable. Among those sinful men there is no one to whom thou canst say, 'This is thy duty. Let thy heart turn to it.' Their settled convictions are that there is nothing in this world that is equal to wealth. The person that would slay such a creature would incur no sin. He who kills him kills one that has been already killed by his own acts. If slain, it is the dead that is slain.