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.
Maya civilization
Maya armies of the Contact period were highly disciplined, and warriors participated in regular training exercises and drills; every able-bodied adult male was available for military service. 
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.
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Maya civilization [SEP] Warriors
During the Contact period, it is known that certain military positions were held by members of the aristocracy, and were passed on by patrilineal succession. It is likely that the specialised knowledge inherent in the particular military role was taught to the successor, including strategy, ritual, and war dances. Maya armies of the Contact period were highly disciplined, and warriors participated in regular training exercises and drills; every able-bodied adult male was available for military service. Maya states did not maintain standing armies; warriors were mustered by local officials who reported back to appointed warleaders. There were also units of full-time mercenaries who followed permanent leaders.