I want to know what were the names of the bows of the warriors of the Mahabharata, their abilities and how they got them
The partial list of names of bows that was mentioned in Mahabharata are :
Krishna : Saranga
Arjuna : Gandiva
Rukmi : Vijaya
Siva : Pinaka
Yudhishthira : Mahendra
Bhimasena : Vayavya
Nakula : Vaishnava
Sahadeva : Aswina
Ghatotkacha : Paulastya
Prativindhya, Sutasoma, Srutakarman, Satanika, and Srutasena : the Raudra, the Agneya, the Kauverya, the Yamya, and the Girisa.
For detailed explanation, see the following passages from Mahabharata.
"Vaisampayana said, '..... And that mighty-armed warrior had obtained also the bow named Vijaya of celestial workmanship, belonging to the great Indra, and which was equal to Gandiva in energy and to also Sarnga (held by Krishna). There were three celestial bows owned by the denizens of heaven, viz., Gandiva owned by Varuna, the bow called Vijaya owned by Indra, and that other celestial bow of great energy said to have been owned by Vishnu. This last (Sarnga), capable of striking fear into the hearts of hostile warriors, was held by Krishna. The bow called Gandiva was obtained by Indra's son (Arjuna) from Agni on the occasion of the burning of Khandava, while the bow called Vijaya was obtained from Drona by Rukmi of great energy.....'
Vaisampayana continued,--".... In thy dream, O king of kings thou wilt behold towards the end of this might the blue throated Bhava, the slayer of Tripura, ever absorbed in meditation, having the bull for his mark, drinking off the human skull, and fierce and terrible, that lord of all creatures, that god of gods, the husband of Uma, otherwise called Hara and Sarva, and Vrisha, armed with the trident and the bow called Pinaka, and attired in tiger skin. And thou wilt behold Siva, tall and white as the Kailasa cliff and seated on his bull, gazing unceasingly towards the direction (south) presided over by the king of the Pitris ......'"
In Yudhishthira's hands was the celestial bow called Mahendra; and in the hands of Bhimasena, O king, was the celestial bow called Vayavya. For the protection of the three worlds Brahman created a bow. That celestial and indestructible bow was held by Phalguni. The Vaishnava bow was held by Nakula, and the bow called Aswina was held by Sahadeva. That celestial and terrible bow called the Paulastya, was held by Ghatotkacha. The five jewels of bows born by the five sons of Draupadi were the Raudra, the Agneya, the Kauverya, the Yamya, and the Girisa. That excellent and best of bows, called the Raudra, which Rohini's son (Valadeva) had obtained, the latter gave unto the high-souled son of Subhadra, having been gratified with him.