Bhoins,
As mentioned by other, you really need to read about the K'Kree in GT:AR. Most of your questions are answered there.
Why did the K'Kree go into space? CT and MT's 'Lords of Thunder' explain that: They were afraid of being eaten. In LoT, the PC's pass down a museum of sorts aboard the G'naak generation ship. Charming videos showing K'Kree being hunted and eaten alive are presented. Once G'naak society on Kirur fell and/or was beaten by the K'Kree, the moon above was still full of those delightful critters. That's a good enough reason to go into space, don't you think?
As for the idea that the K'Kree are still on the 'warpath' somehow, I'm afraid that idea fails even basic scruntiny. They haven't expanded since the Hiver War, they're spread painfully thin across their empire, their worlds are ecological shambles held together by constant effort, and they can barely keep the lid on the territory they already hold and then only by means of genocide.
I'm no K'kree supporter, far from it actually, but the idea that they as a group somehow pose a threat to the other major races is laughable. GT:AR even mentions refugee societies of various g'naak flushed from the 2000 Worlds still 'holding out' on multi-world polities to trailing of the K'Kree. If the Steppelords are as powerful as you believe, why are those worlds still living?
GT:AR also presents the K'Kree trans-rift enclave from the point of view of the Vargr it faces. Put simply, that enclave is a prison that the K'kree cannot expand from and can only maintain at great effort. It is in the best interest of the Vargr that the K'Kree remain stuck to that particular 'tar baby'.
The idea of allowing ihatei to transit the Imperium in order to carve out new lands among the 200 Worlds is a non-starter. Others have pointed out the logistical impossibilities of it - whether you accept them or not - and the Imperium would be insane to plant another population of indepeendent Aslan to trailing. What does the Imperium recieve for this? Yet another cancerous growth on yet another border. Just what the doctor ordered, huh?
You also fail to understand that, unless they arrived in a multi-million sophont wave, the ihatei are doomed. Don't let the idiocy of MT's Alien Incursions foll you. The same book that claims they swamped the Imperial border also bithely states that the majority of ihatei groups number under 10 thousand. Picking off a few thousand Aslan, most of whom are not warriors, from whatever rock they've squatted on inside the 2000 Worlds will be well within the abilities of the K'Kree.
Finally, I wouldn't take the actions of an acknowledged extremist splinter group; the Lords of Thunder, to represent the species as a whole. As an empire, the K'Kree have turned away from expansion and conquest. The upper nobility realizes that their specie's religious goal of wiping the universe clean cannot be achieved. They still make mouth noises to that effect for public consumption, but they've come to a working arrangement with the universe as a whole - we don't expand and you don't come knocking.
Yes, various jihadist groups will still sally out of the 2000 Worlds on their religious quest and, yes, they will make life uncomfortable for those sophonts along the frontier but the 2000 Worlds as a whole will not back them. If you read M:1248 again you'll realize this. Without giving too much away, pay close attention to just what comes of the wreckage of the 2000 Worlds, just how big it is, and what relative little it accomplishes.
I'm not a fan of the K'Kree and usually used them as orc-like cannon fodder for my PCs in those few adventures I featured them. They are nasty, but they are brittle and they can barely control what they've already taken.
Sincerely,
Bill