which languages did they speak?
From the Preclassic period onwards, some of the language groups included Huastecan, Tzʼeltalan-Chʼolan, and Yucatecan among others.
Maya civilization
Proto-Mayan diverged during the Preclassic period to form the major Mayan language groups that make up the family, including Huastecan, Greater Kʼicheʼan, Greater Qʼanjobalan, Mamean, Tzʼeltalan-Chʼolan, and Yucatecan. These groups diverged further during the pre-Columbian era to form over 30 languages that have survived into modern times. The language of almost all Classic Maya texts over the entire Maya area has been identified as Chʼolan; Late Preclassic text from Kaminaljuyu, in the highlands, also appears to be in, or related to, Chʼolan. 
how far back can we trace the mayan culture As far as circa 2000 BC what period of history is that? The Archaic period where were they located? The civilization encompassed areas of south-eastern Mexico, all of Guatemala and Belize, and the western portions of Honduras and El Salvador. did they practice politics? Yes, there were states and chiefdoms which had fluctuating policies towards one another. did they have societies? The society was hierarchical with a sharp difference between the elite and the commoners. did they fight with each other? Yes, clashes were common between states and chiefdoms. what kind of warriors were they? Well trained, and in the Contact period, their armies were highly disciplined where warriors participated in regular training exercises and drills. did they practice trade as well? Yes, and control of trade routes or access to important trade goods contributed to the growth of cities. describe their merchants? Not much is known about them, but it seems that at least some were members of the elite who engaged in long distance trade, while the majority belonged to the middle class largely involved in local or regional trade. did they have market places? Archaeologists have found traces what could have been formal arcade style masonry architectures and foundations of market stalls; and the Spanish colonialists have written about encountering a thriving market economy. can you please describe their buildings Mayan buildings included pyramids and temples, along with large elite residences which took time and heavy manpower to construct, as well as more modest commoner's huts. what materials did they use to build them? The earliest cities were built using stone and some perishable materials, but in later periods, they used limestone, sandstone, lime based cement or fired bricks depending on availability. did they have palaces? Yes, some of them adorned with sculptures.
wiki:15310968
Maya civilization [SEP] Language
Before 2000 BC, the Maya spoke a single language, dubbed proto-Mayan by linguists. Linguistic analysis of reconstructed Proto-Mayan vocabulary suggests that the original Proto-Mayan homeland was in the western or northern Guatemalan Highlands, although the evidence is not conclusive. Proto-Mayan diverged during the Preclassic period to form the major Mayan language groups that make up the family, including Huastecan, Greater Kʼicheʼan, Greater Qʼanjobalan, Mamean, Tzʼeltalan-Chʼolan, and Yucatecan. These groups diverged further during the pre-Columbian era to form over 30 languages that have survived into modern times. The language of almost all Classic Maya texts over the entire Maya area has been identified as Chʼolan; Late Preclassic text from Kaminaljuyu, in the highlands, also appears to be in, or related to, Chʼolan.