This is quite excellent for a first submission. Besides Echo's remark on what should be a rapidly declining population (maybe change it to 4 offspring, 2 of which might be "norma"). Besides that, this needs little changing, methinks. Well done, and welcome to the Citadel!
I have issues with this. First off, there is nothing to differentiate this from every other invincible robot assassin. Except that it is telepathic. And can teleport. And regenerate. And can manipulate the fabric of the universe to stop damage. And can create illusions. And is twice as fast as a human. And can climb on walls. And has magical senses (I thought this was Sci-Fi?) And has a "not very powerful" claw attack that can nonetheless pass through armor as though it were nothing. And supposedly has "time" powers that don't actually have anything to do with time. And is defective, causing it to "kill all fleshies", basically.
So basically, this is a "Robot Sue".
Now, you could do something interesting with this. Maybe its defective, so it has developed intelligence and a conscience, but still is compelled to murder. Since it can shunt damage into alternate versions of itself (that's how I'm reading that anyways), why doesn't it take random damage from other universes itself? These would at least make this a little bit interesting. Also, remove some abilities. Like, a lot of them.
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Welcome to the citadel. You've got some pretty good subs already; just keep working to keep things unique and original.
You know what this reminds me of? The Ship that Sails Between the Worlds, of Moorcock's Elric Saga. A strange, construction that takes our heroes wherever they need to be, without all that pesky wandering. And of course, there could be the seed of a greater conflict here, such that the inn must gather the world's greatest heroes in order to defeat a great evil. An old idea, done in a fresh way. I agree that its not perfect, but it certainly is your best sub yet, Ramhir. Keep it up (And by that, I mean that I wish I were still pumping out subs like you. Don't let yourself run out of steam like me!).
Wait a second... These are a sapient race who breed with normal, unintelligent horses? I don't know, but in addition to the other flaws this post has, that detail just doesn't seem right. Maybe they don't care, but any description of an intelligent species that was fine with getting it on with what would be animals to them, whether or not it makes sense in the context of their history just seems a little weird.
Also, the fact that they "breed" so the Catfolk can sell their offspring seems to imply that because they are not quite as intelligent as other intelligent races, they are being taken advantage of.
Don't get me wrong... There are some good parts of this, but there is definitely some history and other information that needs to improve this.
"Also, they look like horses, which means, since they cannot talk, that the other races will *treat* them like horses"
Then how did the catfolk originally partner up with them? There's some history missing here that could explain some things.
"The Catfolk have also bred up a race of horses that are as far advanced over the Forevergrass horses as the Forevergrass horses are over the normal horses bred by the other races. The other races call them battlesteeds."
You say that the catfolk bred up the Battlesteeds. But then you say that they were created wholecloth from this Lord of Horses breeding with standard horses. So which is it?