During battle, in the top right corner of the screen above the minimap is a series of buttons that will let you pause the game, put it into slow motion, or fast forward. Unless you're playing on the highest difficulty, you can still issue commands to your units while the game is paused which can help you plan out your attacks.
Units run away when they run out of Leadership (think of it as Morale). Having a Lord or Hero nearby buffs Leadership. Getting attacked from the side or back does more damage to Leadership, as does seeing nearby units flee or seeing your Lord die. This can often cause your troops to flee like dominos.
When not part of an army, Heroes can assault enemy armies or settlements and hit them with debuffs (though it costs gold to do so). They also passively apply an effect to whatever province they're standing in (you can see what the effect on their unit card). They can also be placed into armies by moving them to one of your armies on the map. In battle, they are essentially a mini-Lord.
For some general combat strategies, mounted units are usually good for hit and run tactics because they have a high charge bonus. However, they are weak against units with spears as spears deal extra damage to large units and units with spears usually also have charge defense. Using one set of troops to hold the line and another set to get behind the enemy and hit them from the back usually does a bunch of damage to both the enemy health and their leadership.
You generally want to go for the most favorable match-ups you can, so put your units that can pierce armor up against the enemies with armor, your spears up against their cavalry, your ranged units up against their units without shields, your cavalry up against their ranged units, etc.
As for your money, each army you have increases total upkeep by a percentage, so if there is an army you're definitely not using it might be worthwhile to disband it. You can also disband excess troops to save on upkeep. The other option is to demolish some of the buildings in your settlements and replace them with buildings that generate money.
Public Order is lowered by taxes, enemies attacking them or raiding their lands, corruption, and a few other things. It can be countered by stopping taxes, clearing out the enemies, parking a Hero with a Public Order bonus in that province, garrisoning a large army in one of the settlements, constructing certain buildings, or issuing certain Commandments. Commandments can be issued if you own every settlement in a province. Just select a settlement, and then it is a button in the bottom-left in the same spot as the one for changing marching stances for your armies.
I hope this is helpful. These games are a ton of fun, but have a lot of layered mechanics that can take some getting used to.
