Partially answering your qestion:

Why Abhimanyu died in younger age is explained in The Mahabharata, Book 1: Adi Parva: Sambhava Parva: Section LXVII:

And he who was known as the mighty Varchas, the son of Soma, became Abhimanyu of wonderful deeds, the son of Arjuna. And before his incarnation, O king, the god Soma had said these words to the celestials, 'I cannot give (part with) my son. He is dearer to me than life itself. Let this be the compact and let it be not transgressed. The destruction of the Asuras on earth is the work of the celestials, and, therefore, it is our work as well. Let this Varchas, therefore, go thither, but let him not stay there long. Nara, whose companion is Narayana, will be born as Indra's son and indeed, will be known as Arjuna, the mighty son of Pandu. This boy of mine shall be his son and become a mighty car-warrior in his boyhood. And let him, ye best of immortals, stay on earth for sixteen years. And when he attaineth to his sixteenth year, the battle shall take place in which all who are born of your portions shall achieve the destruction of mighty warriors. But a certain encounter shall take place without both Nara and Narayana (taking any part in it). And, indeed, your portions, ye celestials, shall fight, having made that disposition of the forces which is known by the name of the Chakra-vyuha. And my son shall compel all foes to retreat before him. The boy of mighty arms having penetrated the impenetrable array, shall range within it fearlessly and send a fourth part of the hostile force, in course of half a day, unto the regions of the king of the dead. Then when numberless heroes and mighty car-warriors will return to the charge towards the close of the day, my boy of mighty arms, shall reappear before me. And he shall beget one heroic son in his line, who shall continue the almost extinct Bharata race.' Hearing these words of Soma, the dwellers in heaven replied, 'So be it.' And then all together applauded and worshipped (Soma) the king of stars. Thus, O king, have I recited to thee the (particulars of the) birth of thy father's father.

Same chapter further says:

they who became the five sons of Draupadi, those bulls amongst the Bharata princes, were the celestials known as the Viswas.

There might be some story related to them as well.

Why Abhimanyu died in younger age is explained in The Mahabharata, Book 1: Adi Parva: Sambhava Parva: Section LXVII:

And he who was known as the mighty Varchas, the son of Soma, became Abhimanyu of wonderful deeds, the son of Arjuna. And before his incarnation, O king, the god Soma had said these words to the celestials, 'I cannot give (part with) my son. He is dearer to me than life itself. Let this be the compact and let it be not transgressed. The destruction of the Asuras on earth is the work of the celestials, and, therefore, it is our work as well. Let this Varchas, therefore, go thither, but let him not stay there long. Nara, whose companion is Narayana, will be born as Indra's son and indeed, will be known as Arjuna, the mighty son of Pandu. This boy of mine shall be his son and become a mighty car-warrior in his boyhood. And let him, ye best of immortals, stay on earth for sixteen years. And when he attaineth to his sixteenth year, the battle shall take place in which all who are born of your portions shall achieve the destruction of mighty warriors. But a certain encounter shall take place without both Nara and Narayana (taking any part in it). And, indeed, your portions, ye celestials, shall fight, having made that disposition of the forces which is known by the name of the Chakra-vyuha. And my son shall compel all foes to retreat before him. The boy of mighty arms having penetrated the impenetrable array, shall range within it fearlessly and send a fourth part of the hostile force, in course of half a day, unto the regions of the king of the dead. Then when numberless heroes and mighty car-warriors will return to the charge towards the close of the day, my boy of mighty arms, shall reappear before me. And he shall beget one heroic son in his line, who shall continue the almost extinct Bharata race.' Hearing these words of Soma, the dwellers in heaven replied, 'So be it.' And then all together applauded and worshipped (Soma) the king of stars. Thus, O king, have I recited to thee the (particulars of the) birth of thy father's father.

Same chapter further says:

they who became the five sons of Draupadi, those bulls amongst the Bharata princes, were the celestials known as the Viswas.

Why they were killed in younger age is explained in below post:

Upapandavas: Why were they killed?