1) If both your and enemy unit have same initiative, enemy will move first since you`re attacker and enemy had time to prepare for battle.
2) There are about only 2 ways to deal with that problem : increase your initiative, or lower enemy
Onslaught skill (but as you said not enough might runes) , if you find mask of hatred item it lowers enemy init by -1 , heroism banner gives your units 1-3lvl +1 init , snake boots +1 init/speed to all snakes , Anga`s ruby +3 init to all female troops , black dragons also lower enemy units init for -1 , get some units that have higher init (necromancers, archdemons, dragons ...) , battle cry spell (lvl 3 is best since it`s mass). Until then you`ll have to suck it up and mend damage enemy inflicted in that first turn.
3) same as for 1) , when you attack some1 he have time to prepare and react to it idea. Attacking army is coming to you, and your troops are ready and dug in trenches
just waiting to unleash fury on you.
God luck fellow KB player