This took me forever... But here goes, without the accents.
Peasant is "tariacin", "jaduu tariacin", "bertegcin", or "tariad," while peasant woman is "tariacin emegtej"
Militia is "sergijlex" or "cagdaa"
Sword I already gave above, although saber can overlap with it, giving words like "selem" and "ild".
Swordsman is "tujalzuur zadcin," apparently
Lance is "zad" or "gilber," and Lancer is "morin cereg"
Heavy on its own is "dinsger" or "baraan," while heavily armed is "xund zer zevsegtej" or "xund zevsgeer zevseglesen," so I think "xund" might work as heavy as well.
Don't think there's a word that translates into calvary, though "morin cereg," "mor’ton," "mor’toj xun," and "aduu sonirxogcid" apparently all mean horseman.
Bow and arrow is "num sum"
Elite can be "ongo," "sor," "sildeg xeseg," or "deedcuul," though I'm not sure which, if any, of those is the adjective form.
Soldier is "bajldagc", "cereg", or "zanzin", and as a bonus soldiers of fortune are "xolsnij cereg," which could be used for some sort of mercenary group.
Veteran is "xuucin" or "urt nastaj" (The adjective form at least)
Axe is "sux" or "aluurcny sux", battle axe is "bajldaany sux", double axe is "xoer taldaa irtej sux", and hand axe is "culuun sux"
Spear is also "zad," while spear-carrier is "zadcin"
Shortsword I couldn't find... but scimitar is "taxir selem" or "maxir selem"
As for the chinese troops, I forgot to mention that "Jing Rui" means elite. Hope all of the above is helpful... Took forever to translate into mongolian and then translate the cyrillic into latin, which may make for some very strange names. Dunno how that works. Might turn out that none of the above works out. If not... Dunno. I tried my best. Let me know what you think.
