I suspect such a game would get rather spreadsheety.
I do get tired of this argument, used over and over. Games are at their core rules and numbers. You can spreadsheet plan all day but if your opponent does one unexpected thing, you have to spreadsheet plan another day.
Will events be turned off, being a RNG type thing?
Trashy idiot-designed poorly implemented events are turned off to begin with and stay so yes

.
Any chance of a 'click on visible enemy unit and check their odds against your units' function?
I don't know, I'm only doing the xml stuff, my friend is doing the DLL. We only just started this so that isn't a priority just yet. However, because defensive bonuses are known and you can see their promotions, you should at MINIMUM be able to figure out "will I win or lose if that attacks" in your head even without such a UI. The UI would still be nice though.
Waiting for reinforcements and it's safer to stay fortified on a hill than to run home with cavalry nipping at your heels? Exploiting the AI to get that next GG you need to deploy units at 11xp, whilst keeping its hammers pouring down the drain? Keeping a Settler away from Iron? You've pillaged a frontline Horse and need to stop them reconnecting it, and whilst keeping the stack safely reinforcing are taking the opportunity to exploit 51% autokills?
You're basically telling me you can abuse the AI because it's bad at war. I'm not asking about a better AI mod here. Even in the base game you can perma-lock the AI off resources (it won't attack even a trivial force next to a resource) :/. Every time you win a "guaranteed" battle in enemy territory it will throw your great general well under 50% health. If you want to "farm" off that one unit, you're going to spend a lot of turns paying a lot of out-of-borders maintenance and healing (slower in enemy territory) instead of attacking to do it...and no matter how strong that unit gets, you're still some collateral and a few mounted from total stack wipe. I'm not seeing the issue here.
If you want to kill your trade routes with the target, pay more than a city's worth of

/turn in maintenance (you need multiple units to protect your GG) on top of lost trade routes, hurt relations, and increase AI war targeting priority on you (its backstab war plan check) all for granting XP to one unit, I don't see how that breaks the game at all. It's a silly example, there's no way around it.
It's not an extraordinary situation for a pair of hostile CR stacks to come up against one another, is it?
Whether you let them take the city then retake it is a function of expected hammer loss from either, along with some consideration for war success and the importance of said city (also hills completely negate CR I for example). If you have the units to follow-up/kill 5 axes at .5 hp though it might be worth taking that trade instead, especially if you can use pop you'd have otherwise lost to simply whip a 6th unit.
Has the playtesting covered many UUs? Off the top of my head, Praetorians, Vultures and Dog Soldiers have interesting combat scores against their contemporaries that might raise eyebrows when autokills are thrown into the mix.
Prats are devastating when they outnumber you and completely hosed when materially outnumbered. They will beat a non-aggressive axe straight up, yes, but they will do so with so little strength that even something like an archer or even a warrior can kill them easily. 1-2 catapults and a stack of prats can get completely wiped by regular combat I axes. They also can't attack equal number or even fewer axes in a city with much success/momentum, since axes will always kill them if they have fortify, 20%, or anything else to give them that last little boost over the prats. What do the prats do then? Run around in enemy territory trying to pillage while the axes guy builds more units and swarms them to death for far less total

invested? That doesn't sound like a winning move to me.
Don't forget that vultures lose to axes in pitched battles, while dogs are soft to both archers and chariots. However, each of these uniques brings a special ability to the table in deterministic battles; vultures are more likely to get a winning draw against non-axe defenders while dog soldiers complete hose all opposing melee in the era without fail.
I'm a bit saddened at the continued irrational stigma against prats relative to other top-tier UU. Really, prats and vultures come to mind, but not FIRST STRIKE IMMUNE war chariots under these rules? War chariots are complete hell unless there are spears, although I suppose that was always true (they are better than prats in the unmodded game also).