1) Mahabharata Researchers say 1 rule. In history, if there is something, it is an evidence. This something can be accessed to derive a meaning. If there is nothing, then it does not mean anything. History is not logic. History means, it happened. It happened, so there must be some evidence. Well this rule should be applied to Mahabharata too. Till there is some archeology evidence, Mahabharata has no meaning in History. Mahabharata can be a great text. But, Archeology evidence is required to consider Mahabharata as history and make chronology from it.
2) Regarding 3102 BCE Kali, 3076 BCE Yudhisthira Saka, 3667 BCE Saptarshi Era, there are no inscriptions written before 100BCE as public records. Heliodorus pillar (dated in 2nd century BCE), names sankarshana Vāsudeva. It even exhibit a verse traceable to Mahabharata. So Mahabharata was well known. But doe’s not use Kali to date it. instead, it dates the writing in kings accession year and not Kali. Nanaghat royal inscription of Sathavahanas also names Balarama & Vāsudeva krishna. It does not use Kali epoch. Absence of evidence for Kali, Yudhisthira or saptarshi means, it was not known before 100BCE. So, first prove, it was in practice before arguing Mahabharata based on Kali epoch.
3) Guru cycle is 12 years. Shani cycle is 30 years. Other planets has faster (lesser in time) cycles. LCM is 60 years. So, we have 60 Samvatsara as a larger year cycle rather than a century (100 years). On an average we can expect 2 kings rule in one samvatsara. 100 king rule means 3000 years. Someone around 110BCE, thought next imperial king is 100th king in Kaliyuga. Vikramaditya (of Vikrama Shaka) takes birth. Varahamihira fixes kali 3000 years before. This 3000 year difference (3101 - 101BCE) between Kali and Vikramaditya birth, gives a suspicion that, it was a calculated figure. A birth was not controlled and hence it can’t be exactly 3000 years. Western jesuits working with Indian calendars probably did not understand 101st king. They used 101 from king vikram’s birth, while finalising Jesus Era (1 CE). Do, we get Kali in 3101BCE. If you are a Mahabharata researcher, you have to explain this perfect number 3000.
4) Charriot wheel question? Sanauli, UP archeology find, conservatively dates war chariots to 2000-2200BCE. The war chariot has solid wheels. The wheels had copper fixtures to avoid wheel from cracking. So, it was not a fast moving chariot. Fast moving horse drawn chariots, like the one used by Arjuna and Krishna has to be spoked wheel chariot. So, first prove spoked wheel in your MB date (3K or 5K) before arguing Mahabharata war in 3K or 5K BCE dates.
Lower bound for Mahabharata : is 2nd century BCE. By this time, Mahabharata and Vāsudeva Krishna were known to common people of India. Heliodorus pillar mentioning Krishna also validates the same.
5) We have one English word called “Barbarian’s”. This has come to English from Greek via Romans. It means savages. Greek word was Barbaras. In Mahabharata, we have the same Barbaras (in Sanskrit) fighting Mahabharata war along with Saka, Parthia, yavana etc. These tribes were ruling beyond Kabul valley in north west of India. Check MB reference below. Actually these Barbaras were Babylonians. They were called by the name Babiraus, in old Persian (DNA inscription of Darius the great). Unless Babirus introduced themselves as Barbaras, to both Greek and Indians, the name can’t be same in Greek and Sanskrit. No other Barbaras identified in this region. Babylon comes up after 2000BCE. If Barbaras/Babylonians has to fight in 3K or 5K MB, please prove babylons existence in your MB date. Same thing with Parthia. MB says, all these were warrior tribes born out of Nandini, when kartyaveeraarjuna tries to capture that holy cow. Let them take birth from any form. You need to prove their existence archeologically first.