I wish to know historically when the Chinese might have known about the Mahabharata/Ramayana

Here's a reference to a recent and complete translation:

http://www.sasnet.cn/english/news/showcontent.asp?id=16

Chinese version of Mahabharata published in Beijing

The Chinese version of the great Indian epic, Mahabharata, was published in Beijing in December, 2005. Seventeen years have passed since the beginning of the translation work in 1989 which had been initiated principally by Professor Jin Kemu (1912-2000) and Professor Zhao Guohwa (1943-1991). Thanks to the contribution of another Sanskrit scholar Xi Bizhuang they finished the translation of the first parvan of the epic that was published at the end of 1993. Subsequently, however, the work was interrupted partly due to the death of Professor Zhao in 1991, to be resumed under the sponsorship of the Chinese Academy of Social Sciences in 1996. The project-team of 5 members was headed by Professor Huang BaoSheng, Director of the Institute of Foreign Literature Studies, CASS, to which four of the members (Huang Baosheng, Guo Liangyun, Li Nan and Ge Weijun) also belonged, whereas one team-member (Duan Qing) was from Peking University. The original work on which the Chinese translation was based was the Critical Edition of Mahabharata, published by Bhandarkar Oriental Research Institute, Poona, with Vishnu S. Sukthankar, S. K. Belvalkar and P. L. Vaidya successively as its editors-in-chief. Since it was not easy to convey the exact meaning of the original in Chinese verse, the prose style was chosen as a more appropriate translated rendering. For the sake of terminological uniformity, names of heroes, places, weapons, plants, etc., a Sanskrit-Chinese glossary was prepared before commencing the translation, which was continually appended as the work proceeded, to avoid having divergent translations of the same term. Efforts have been made to correspond to ancient translations of Buddhist scriptures to lend this modern version an antique flavour. Given that most Chinese readers are not familiar with the cultural and historical background of the stories and concepts of Hinduism, the text is accompanied by necessary annotations. Though translation work of the 18 parvans was completed in 2002-03, more than two subsequent years were spent in revising and proofreading. Whereas Professor Huang was responsible for the revisions and for authoring the introduction to the complete work, the proofreading was done by both professional proofreaders and the translators themselves. The Chinese version of the Mahabharata is in six volumes and is published by the Chinese Social Science Publishing House.