Order of Battle

If there is a battle, in which order do the different types of units (main attack, building defense, ground stealth, rare units e.g.) go into battle? Is there a fixed order or it is solely dependent on the values of the units?

If you're attacking, your units with the highest attack will attack first until they all die or you win. After that your second highest will attack and so on. The defender's unit with the highest defense will defend first similarly.

If you have multiple units that are tied in att/def then it randomly picks which one attack or defend.

In encounter battles, you take turns attacking and defending. What this means is that first your highest attack unit attack. Then your highest defense unit defend. You and the enemy swap back and forth attacking and defending in encounter battles.
If there is neutral units involved in the battle. You take turn attacking the neutral units and attack/defending from your enemy in the encounter. Neutral units always roll for defense.

Just here to add more info about what WD said, if im not wrong when multiple type of units with same att are attacking the one with highest crit attacks first if they have same crit then i think its random.
Also there are some exceptions to what WD said most of these happen when you chain or combine units that are on field which make your stack attack and defend at the same time, highest deff goes first and same with att but yea this is bad if you have an stack full of offensive units or viceversa. example: you have a wall of 4 units and you use it to attack or tb one stack and at same time you use a big stack that was in a city to attack this same stack, well if your enemy attack this wall and you were unlucky and didnt tb enemy's stack then most likely you gonna face a att/def battle which you gonna attack and deff at same time.