@Thunderbrd
1. Stomp could be possibly a large Bludgeon Damage with the fact that neither unit can move. Because one is pinned down and the other is stomping. Note one could possibly dodge the stomp too.
2. Cool! Bison or Deer riders could possibly get this too. Since they have Horns and Antlers.
3. Yeah its probbly just the same thing.
4. Well in the video I provided they picked up the enemy troops and they pulled them apart. They could also potentially throw an enemy too. Thus using them as a projectile to hit other troops. Thus maybe you might want to have "Throw" which can make non Archery/Siege units able to throw projectiles if engaged in battle with a unit. Note this unit would have to be smaller thus no throwing other elephants or horses.
5. Yeah sort of a "city bombard" mixed with "pillage tile", but no money from the "pillaged" tile.
6. In games like D&D they have Piercing, Bludgeoning or Slashing for types of attacks. Are you going to have the same? Also they have element attacks. While most would not apply to us I know that some might such as ...
- Fire (Arsonist, Flamethrower, etc)
- Poison (Or even Acid)
- Gunpowder
- Explosives (ex Grenades, Mines)
- Electricity
- Sonic
- Non-Lethal (Not sure if we need this)
- Future Weapons (ex. Laser, Plasma, Anti-Matter, etc)
1. I'll think more on that for a bit. Civ's quickly resolved battle system makes it tough to really bring home what's happening in a combat so it takes a lot of work to figure out how to make an effect as entertaining in play as it ought to be. So systems must be evocative from the player observer's distant and approximated viewpoint. Thus I'm trying not to get to tricksy with combat effects that manipulate things inside the scope of the rapidly resolved civ combat unless it can make an obvious and big difference in how things played out when you look at the combat log.
So some ways units fight are still approximated into the strength and general combat ability of the unit. Perhaps what should become a part of the 'next round' of combat mods down the line would be a size definition on units and Stomp would be a promo line for large units that increases their strength drastically against units smaller than they are. Perhaps not as definitive as what you suggested there, but the idea with much of these adjustments are to evoke the imagination to fill the blanks anyhow. (If stomp changed the animation graphic of a unit in combat that would carry the strongest possible impact too.)
2. And Rhinos of course

Gore would become a line of promos available to such savage attack styles like horns, and possibly even axe lines. It would improve chances of rendering a critical injury on the defender... I may have to adjust my take on criticals now - I was going to make it like afflicting in that it takes place at the end of the combat, but perhaps I need to make it possible to receive a critical injury every round (with an EXTREMELY low chance each round though...) I'll probably make the base chance of receiving a critical injury something like 1/10th of the damage taken. Most damages stretch between 5 and 20 or so so this means .5 - 2% chance range per round of combat which seems appropriate. Modified by Gore and perhaps other promo lines which have an iCriticalHit value representing a percentage increase in the chance per round you inflict damage of inflicting a critical.
Criticals, once inflicted, will be an ever developable list of affliction promotions and it will randomly select one out of the list without weighting any particular selection. Criticals would be like Broken Leg, or Busted Ribs, or Deep Gash... etc...
3. I was thinking about trample earlier... I realized it could be an effect where once you've dealt a certain amount of damage (100 - the trample damage), you 'withdraw' (or rather move on through) and go on to attack the next best defender. This would make the ability an advanced and more controlled version of Stampede. I'd need it to have a second value though to determine the maximum # of such attacks it would make. I'll save it for additional Combat Mod addons to come but its very feasible to do this.
4. This'll need a bit more thought but would probably be contingent on setting up the size categories of units first.
5.Part of an additional combat mod installment to come is a plan for a 'destructive' tag to go on some units that makes it so that when they attack a city, a local building is randomly targeted and must check against possible destruction based on that building's value for that (for when cities are taken) vs the destructive power of the unit. An advanced version for siege would be to target specific buildings this way when bombarding. This destructive value could also become a percentage chance to destroy an improvement on a tile you're attacking too (which would mean I should put a toughness value on improvements too...).
I could also work into that plan a tag that makes units reduce city % defense when they attack (in case you get a bit too impatient to wait a round to clear out that last bit you're cats couldn't quite get rid of.)
6.At the moment, there's no plan to really fully differentiate unit damage types much beyond some additional effects that may be encountered with certain types of damage.
Flame wielding, explosive and toxic gas units would have Knockback to force defenders out of their defensive positions, eliminating fortification bonuses and forcing defenders in an open field setting to flee if possible.
Poison isn't really damage but an infliction of an affliction promotion on the enemy: effects can be extremely varied.
I didn't find it necessary in the scope of civ to get into piercing/bludgeoning/slashing (at least not yet) as simply working in Puncture vs Armor and Precision vs Dodge worked quite well to encapsulate those things with enough variety. Perhaps down the road once those have been fully balanced into the unit scheme we can look at further complexity.
I have an idea for cold damage to reduce precision and dodge values but its a rough concept at the moment and probably won't make it quite into this first combat mod segment.
Most other forms of damage you mentioned there aren't widely used throughout history, with perhaps the exception of acid which could be designated as an anti-armor poison. The future could start really opening up those options so perhaps more to come there such as electricity weapons causing a stun effect etc...
Also, one way we COULD define the differences in Slashing, Piercing and Bludgeoning would be again, Subcombats. Make them Combat Classes and give armors specific modifiers against those types. AND/OR make general armor types like 'Chain/Leather/Plate etc...' combat classes (you can add a combat class to a unit when it gets a promotion and it can lose that combat class when that promotion goes away or is overridden. And then give each damage type standard bonuses and penalties vs given armor types.
If you want to arrange that it will be possible. There aren't tags for Puncture, Armor, Precision or Dodge modifiers VS particular combat class types (maybe down the road) but general combat modifiers vs combat class types can be given to various equipment promos of course.