Yeah, controls work surprisingly well for the small screen.
There's no experience points or leveling up. You get new, more powerful units to work with every few battles. It's not an RPG - it's more like chess with D&D characters. Summoner is my favorite - he can transform trees and rocks into monsters.
The player and cpu controlled archers have the same abilities. Archers can shoot from behind trees, rocks or other units - something the computer will use to its advantage. You can hide behind a tree, using it for cover and shoot at other archers without having to worry about being hit. Or you can stack two archers next to each other for double fire power, hide an archer behind a beefy soldier, etc.
The support page has a pretty good FAQ with description of units and tactics. Also, are you planning on adding more skirmish maps? (it looks like you have space to list more

)
One thing that helps a lot is getting a sense when to press the attack. You can usually retreat to get computer opponents to follow you out into the open, then swarm them.