1.If you CAN do training, you should keep doing training for now. Once you hit 200 honor, you can take a guard test, and can play against other factions, where the meat of the game is. Once you get that far, take advantage of Novice, as it's the only rank where you'll keep what you find, even if you lose.
2.The only way to gain more honor from farming is to set the secondary condition from "K.O's" to "Overall" and do everything at least once (Beat troops, Beat Officers, use flasks, and capture bases). You also have to allow the game's time limit to run out, and of course, you have to win.
3.There is no best mode for liutenants. Liutenants will appear more often the more players there are in the match, and will appear much more often when there are opponent players. I'm not sure if you can even find liutenants in training as it's been a long time since I've started the game, though I'm sure you can.
I hope this info helps you out, and welcome to DWO.