So is there any known way to give the "life" back to someone dead?
Yes, there is a way to give back the life to some dead person according Hindu scriptures. The name of such vidya is Sanjivani (re-vivification). Mentions about Sanjivani is mentioned in many Hindu scriptures.
Shukra, teacher of Asuras, is a master of Sanjivani vidya and he used it to bring back to life many dead people.
It appears somewhere in Mahabharata it is mentioned that Krishna gave
back life to someone dead. Is it true?
It is mentioned in Mahabharata that Sukra gave back life to many dead asuras and Kacha usning Sanjivini. Similarly Kacha gave back life to dead Sukra using Sanjivini (gained from Sukra). I am not sure whether Krishna used Sanjivini anywhere.
Section 73 of Sambhava Parva of Adi Parva of the Mahabharata has mentions about Sanjivani vidya several times
"Between the celestials and the Asuras, there happened, of yore,
frequent encounters for the sovereignty of the three worlds with
everything in them. The gods, then, from desire of victory, installed
the son of Angiras (Vrihaspati) as their priest to conduct their
sacrifices; while their opponents installed the learned Usanas as
their priest for the same purpose. And between those two Brahmanas
there are always much boastful rivalry. Those Danavas assembled for
encounter that were slain by the gods were all revived by the seer
Sukra by the power of his knowledge. And then starting again, into
life,--these fought with the gods. The Asuras also slew on the field
of battle many of the celestials. But the open-minded Vrihaspati could
not revive them, because he knew not the science called Sanjivani
(re-vivification) which Kavya endued with great energy knew so well.
And the gods were, therefore, in great sorrow. And the gods, in great
anxiety of heart and entertaining a fear of the learned Usanas, then
went to Kacha, the eldest son of Vrihaspati, and spoke unto him,
saying, 'We pay court to thee, be kind to us and do us a service that
we regard as very great. That knowledge which resides in Sukra, that
Brahmana of immeasurable prowess, make thy own as soon as thou canst.
Thou shalt find the Brahmana in the court of Vrishaparvan. He always
protects the Danavas but never us, their opponents.............
"Sukra hearing this said, I will revive him by saying, 'Let this one
come.' Then having recourse to the science of reviving the dead, Sukra
summoned Kacha. And summoned by his preceptor, Kacha appeared before
him in the gladness of heart tearing by virtue of his preceptor's
science the bodies of the wolves (that had devoured him). And asked
about the cause of his delay, he thus spoke unto Bhargava's daughter.
Indeed, asked by that Brahman's daughter, he told her, 'I was dead. O
thou of pure manners, burdened with sacrificial fuel, Kusa grass, and
logs of wood, I was coming towards our abode. I sat under a banian
tree. The kine also, having been brought together, were staying under
the shade of that same banian tree. The Asuras, beholding me, asked
'Who art thou?' They heard me answer, 'I am the son of Vrihaspati.' As
soon as I said this, the Danavas slew me, and hacking my body into
pieces gave my remains to jackals and wolves. And they then went home
in the gladness of heart. O amiable one, summoned by the high-souled
Bhargava, I after all come before thee fully revived.'
"On another occasion, asked by Devayani, the Brahmana Kacha went into
the woods. And as he was roving about for gathering flowers, the
Danavas beheld him. They again slew him, and pounding him into a paste
they mixed it with the water of the ocean. Finding him long still (in
coming), the maiden again represented the matter unto her father.
And summoned again by the Brahmana with the aid of his science, Kacha appearing before his preceptor and his daughter told everything
as it had happened. Then slaying him for the third time and burning
him and reducing him to ashes, the Asuras gave those ashes to the
preceptor himself, mixing them with his wine. And Devayani again spoke
unto her father, saying, 'O father, Kacha was sent to gather flowers.
But he is not to be seen. It is plain he hath been lost, or has died.
I tell thee truly, I would not live without
Vaisampayana continued, 'Receiving the
science imparted to him by his preceptor the handsome Kacha, ripped
open his stomach, came out like the moon at evening on the fifteenth
day of the bright fort-night. And beholding the remains of his
preceptor lying like a heap of penances, Kacha revived him, aided by
the science he had learned...........
You can also read this answer for one more instance of using Sanjivani by the same Shukracharya from Garga Samhita.