For your animation question, as long as you don't trigger that animation, missing said animation should be fine. You can see this by disabling Parry and removing all parry related animations. Same should work if you remove bounce animation and ensure no attacks cause bounce. There might be an issue with a couple standard animations that you never see, but using a default animation for that should work as a quick fix.
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The way I see it, there's three things from Smash you'd want to look into. Attack/combo system, health/percent system, and the platforming system.
Attack/Combo system
The attack/combo system should be fairly easy to copy, with minimal code changes. It's mostly your attack data, and a low-ish movement friction. If you want DI for falling characters, you'll need to alter code in ControlsScript for that (it is a bit of work, but shouldn't be too hard). You'll probably want to add a new variable in CharacterInfo's PhysicsData for DI (controlling how much influence they have with DI), and use that in the ControlsScript DI code.
Additionally, check this post about editing the combo counter to be live updated instead of after the combo finishes. If you want to be exactly like Smash, you can remove combo text display altogether.
Health/Percentage System
For the health system, you'll definitely need to alter code, and you'll also need to integrate it into the knock back physics of each character. Essentially it's a new health system. I'd create a new variable for hit percentage, don't use Life Points as that could create more issues. Those variables should be added to CharacterInfo, but you'll need to change corresponding functions in ControlsScript (each hit adds percentage instead of damaging Life Points, and percentage also affects knock force).
Oh, and slightly related would be the rounds system tweaked with stock/time instead. Unless you want unique stock values for each character, I'd put this into a global config class, probably Round Options. While there, you can also change Spawn positions from float to Vector2 (for height) to prepare for platforms...
Platforming System
But to me, the hardest part is the platforming aspects (multiple platforms you can jump through from below, and the kill zones at far edges of the world space). UFE is base on traditional 2D fighting game mechanics, which doesn't have multiple grounds. You would need to completely alter how UFE handles jumps and registers ground states.
For the killzone, your best bet is to create a manager that tracks all on-screen character's positions and just triggers appropriate KO animations/functions when they reach stage limits (which you'd have predefined in the manager script - could also be specific to the stage). You won't be able to use Unity's OnTrigger since there are no rigidbodies / colliders on UFE characters (hitboxes aren't colliders).
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Looking at the video MisterMind posted on Unity forums, they managed to get everything except the multiple platforms bit. However, they got the killzones (at least at the bottom), so that's a good start.
There's also this post from PsychoGames a while back. He's made a small start by looking at IsGrounded() in PhysicsScript (where I'd start looking to), but not sure of his progress since.
Honestly, each of these systems is pretty much worthy of their own thread! Normally, I try testing ideas myself and posting my findings. But "make UFE like Smash" isn't a 10 mins coding task . It's likely going to take a while to get everything working right. If you can design your game to work without multiple platforms (like the video), then it's probably not as daunting a task since you're not not altering so much base code.
Good luck! If you're desperate, or get really stuck, keep posting here and I'll try to pitch in where I can.