What is the importance of Sacrifice (Yajna) or austerities ?

By performance of yajnas, all activities become purified, as it is stated in the Vedas:

ahara-suddhau sattva-suddhih

sattva-suddhau dhruva smritih smriti-

lambhe sarvagranthinam vipramokshah.

Performance of yajnas has many benefits

By performance of yajna one's eatables become sanctified

By eating sanctified foodstuffs one's very existence becomes purified; By the purification of existence finer tissues in the memory become sanctified, and when memory is sanctified one can think of the path of liberation.

In Bhagavad Gita (BG) Lord Krishna explains to Arjuna

BG 3.16: My dear Arjuna, one who does not follow in human life the cycle of sacrifice established by the Vedas certainly leads a life full of sin. Living only for the satisfaction of the senses, such a person lives in vain.

As explained by Srila Prabhupada

Yajna or sarcifice for the current  Age of Kali is the sankirtana-yajna (Kirtan- chanting of the Holy name) is recommended by the Vedic scriptures, and this transcendental system was introduced by Lord Caitanya for the deliverance of all men in this age.

How to achieve real peace ?

In Bhagavad Gita (BG) Lord Krishna instructs to Arjuna,

BG 2.70: A person who is not disturbed by the incessant flow of desires -- that enter like rivers into the ocean, which is ever being filled but is always still -- can alone achieve peace, and not the man who strives to satisfy such desires.

BG 2.71: A person who has given up all desires for sense gratification, who lives free from desires, who has given up all sense of proprietorship and is devoid of false ego -- he alone can attain real peace.

BG 2.66: One who is not connected with the Supreme [in Krishna consciousness] can have neither transcendental intelligence nor a steady mind, without which there is no possibility of peace. And how can there be any happiness without peace?

BG 5.29 and Svetasvatara Upanishad 6.7

People are anxious to attain peace in the material world. But they do not know the formula for peace, which is explained here. "Men should offer everything to the transcendental service of the Supreme Lord because He is the proprietor of everything."

Isopanishad

Iso 1: Everything animate or inanimate that is within the universe is controlled and owned by the supreme Lord. One should therefore accept only those things necessary for himself, which are set aside as his quota, and one should not accept other things, knowing well to whom they belong.

What is the cause of disturbed mind?

Bhagavad Gita(BG) Lord Krishna says to Arjuna

BG 2.60: The senses are so strong and impetuous, O Arjuna, that they forcibly carry away the mind even of a man of discrimination who is endeavoring to control them.

BG 2.62: While contemplating the objects of the senses, a person develops attachment for them, and from such attachment lust develops, and from lust anger arises.

BG 2.63: From anger, complete delusion arises, and from delusion bewilderment of memory. When memory is bewildered, intelligence is lost, and when intelligence is lost one falls down again into the material pool.

BG 2.67: As a strong wind sweeps away a boat on the water, even one of the roaming senses on which the mind focuses can carry away a man's intelligence and can disturb the mind.

What is Yoga?

In Bhagavad Gita Lord Krishna instructs to Arjuna,

BG 2.48: Perform your duty equipoised, O Arjuna, abandoning all attachment to success or failure. Such equanimity is called yoga.

BG 6.2: What is called renunciation you should know to be the same as yoga, or linking oneself with the Supreme, O son of Pandu, for one can never become a yogī unless he renounces the desire for sense gratification.

Who is a successful Yogi ?

BG 2.56: One who is not disturbed in mind even when there miseries or happiness, and who is free from attachment, fear and anger.

BG 2.57: One who is unaffected by whatever good or evil he may obtain, neither praising it nor despising it.

BG 2.58: One who is able to withdraw his senses from sense objects, as the tortoise draws its limbs within the shell

What is the purpose of knowing Vedas?

Bhagavad Gita.(BG)Lord Krishna instructs to Arjuna as follows:

BG 2.46: All purposes served by a small well can at once be served by a great reservoir of water. Similarly, all the purposes of the Vedas can be served to one who knows the purpose behind them.

Further Lord Krishna says:
BG 15.15:
vedaiś ca sarvair aham eva vedyo vedānta-krd veda-vid eva cāhamBy all the Vedas
I am to be known. Indeed, I am the compiler of Vedānta, and I am the knower of the Vedas.

Srila Prabhupada

Vedānta mean the last word in Vedic wisdom, and the author and knower of the Vedānta philosophy is Lord Krishna; and the highest Vedāntist is the great soul who takes pleasure in chanting the holy name of the Lord. That is the ultimate purpose of all Vedic mysticism.

Does Violence has any utility?

Manu-samhitā- 

The lawbook for mankind, says a murderer should be condemned to death so that in his next life he will not have to suffer for the great sin he has committed. Therefore, the king's punishment of hanging a murderer is actually beneficial.

Srila Prabhupada
Everything has its proper utility, and a man who is situated in complete knowledge knows how and where to apply a thing for its proper utility. Similarly, violence also has its utility, and how to apply violence rests with the person in knowledge. Although the justice of the peace awards capital punishment to a person condemned for murder, the justice of the peace cannot be blamed, because he orders violence to another person according to the codes of justice.

What are qualities of Soul?

Bhagavad Gita

BG 2.20: For the soul there is neither birth nor death at any time. He has not come into being, does not come into being, and will not come into being. He is unborn, eternal, ever-existing and primeval. He is not slain when the body is slain.

BG 2.22: As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones.

BG 2.24: This individual soul is unbreakable and insoluble, and can be neither burned nor dried. He is everlasting, present everywhere, unchangeable, immovable and eternally the same.

BG 2.25: It is said that the soul is invisible, inconceivable and immutable. Knowing this, you should not grieve for the body.

The Śvetāśvatara Upanisad (5.9 )In the Mundaka Upanisad (3.1.9)
Size of the soul is described as one ten-thousandth part of the tip of the hair.
Very very minute....

Katha Upanisad (1.2.20)
There are two kinds of souls — namely the minute particle soul (anu-ātmā) and the Supersoul (Parmatma). Both the Supersoul [Paramātmā] and the atomic soul [jīvātmā] are situated within the heart of the living being,like two birds sitting on the same tree.

Is Soul separate from body? -Learn it from a Neurosurgeon.

"Yes, Soul is separate from body "--Dr.Hamilton

This and much more details about the soul  are mentioned in Bhagavad Gita and Vedas...more than 5000 years ago!!!!!

What happens after death?

Bhagavad Gita

BG 2.13: As the embodied soul continuously passes, in this body, from boyhood to youth to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change.

BG 2.22: As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones.

Who is Guru or spiritual master?

(Caitanya-caritāmrta, Madhya 8.128)

Sri Caitanya Mahaprabhu said that one who is master in the science of Krishna consciousness, regardless of his social position, is the real spiritual master.

kibā vipra, kibā nyāsī, śūdra kene naya
yei krishna-tattva-vettā, sei 'guru' haya

"It does not matter whether a person is a vipra [learned scholar in Vedic wisdom] or is born in a lower family, or is in the renounced order of life — if he is master in the science of Krishna, he is the perfect and bona fide spiritual master." So without being a master in the science of Krishna consciousness, no one is a bona fide spiritual master.

Padma Purāna

"A scholarly brāhmana expert in all subjects of Vedic knowledge, is unfit to become a spiritual master without being a Vaisnava, or expert in the science of Krsna consciousness. But a person born in a family of a lower caste can become a spiritual master if he is a Vaisnava or Krishna conscious."