There's definitely historical context here. A lot of these disputes were (obviously) resolved by the government of the People's Republic, which I believe the ROC refuses to recognize and thus also won't drop the claims.
I understand the PRC claims along with the PRC's border disputes(except for Arunachal Pradesh) but why do they claim parts of Russia, Pakistan, and Even Kazakhstan?
Yes, and in addition to that, the treaties that the PRC made over these disputes may have been something the ROC would have done as well, but recognizing the treaties would mean recognizing the PRC, and other countries can’t make treaties with a country that the PRC won’t let them recognize.