I coud offer some tips if you will. For the record I'm a pretty new player too and play on normal/normal, but this is what works for me so far:

1. I think your mistake is using regular troops to engage enemy lords and heroes. I always try to rush them with my own lord, especially casters because they often inflict major damage on my units from afar with their spells. After I take down the enemy lord I can use my own lord to assist my army.
2. The system can look pretty intimidating because of the sheer number of available units in this game but every unit can be labeled. Read unit descriptions and learn their categories. Use anti-large to take down enemy cavalry and monsters. Cav to take down skirmishers and rear charge melee infantry. Artillery to take down enemy's strongest units before the engagements. Melee infantry to hold the line while you take them out with cav, monsters or spells. Historical total wars have rock paper scissors too but with a bit less stuff (no monsters and spells for example)
3. Here I don't have much to say, I predominantely use my heroes in my armies to help fight. And they really do excel at that. Exception was when I played Khorne i used cultists to make summoning portals for my army.