Tyranids create Warp Shadow, so I doubt they feed the Chaos Gods.
The Necrons hate the Warp and everything to do with it, and were basically made to try and fight the Warp(which is fed by living things, and is the hell it is now because the Old Ones used it as a weapon in their war against the C'Tan, and since Orks were made to fight the C'Tan, and have a unique(but still applicable) relationship woth the Warp, I doubt they don't feed Khorne. Probably not as much as forces of Chaos or humans fighting, but still.
Kroot are technically mercenaries, actually, and give their services to other races as well, if hired. I'm guessing the Tau just haven't bothered yet since they think of the Kroot as barbaric(cannibalism and not being Tau does that. They can be pricks at times).
As for what I disagree with and why;
The overstretch thing is something I agree with; they're supposed to be starting their Third Sphere Expansion anyway, and without good FTL travel, they're going to have difficulty with that. However, as their technology is still advancing, and they will be grabbing a rather large amount of Imperial Technology, and they have the Nicassar/human psykers(the Black Ships ain't collecting no more on Tau worlds, so they'll have to find a way to deal with psykers), so they stand a good chance of developing some better means, though they'll probably try and avoid the horror-circus that is Imperial travel. Don't forget; because of their crappy FTL travel, each world is a lot more self-sufficient than in the Imperium. And more efficient, typically with less people. They'll be doing a lot of 'terraforming' and population control on newly assimilated Imperial worlds, I can tell you that much. Which may, in turn, start to slow them down, but they're efficient enough that I doubt it will make much of a difference before they'd be forced to slow down anyway.
Also, Giglamesh, the Horizon Accelerator Engine(near light-speed) was what allowed the Second Sohere Expansion; nearly a thousand years ago.
They've come a long way since then. It says in the codex that their propulsion systems were enhanced further to reach "hitherto unthinkable velocities".
They can probably travel significantly faster than light now, especially since the time between the official start of the Third Sphere Expansion, and the claim of the first new Sept is less than a third of a year. Or, if ou get the feeling that that one had been in progress for a while anyway(like I do), the annexation of T'Ros/Taros took about a year. So yeah, they have FTL now. Not as good as Warp travel(when you're lucky with the Warp, that is...), mind you, but they certainly have it. They probably have FTL communication too, through the use of ansibles or something similar. Look it up. It's a thing that's theoretically possible, with quantum entanglement.
As to the whole Chaos cults thing; why would there necessarily be more activity? Especially since the water caste and the better living quality means people feel less of a need to turn to chaos cults, and the instilled fear of mutants and psykers instilled in the Imperial Populace, while the Tau aren't close enough to the Warp to turn to Chaos through 'natural' means. There would likely be a brief reactionary surge with psykers not being persecuted as much, right before the Fire Caste suppressed any signs of Chaos rather messily. And then the Ethereals would proclaim what was to be done about psykers henceforth. Obviously the Tau know about the Warp, with the way their ships get so fast(I think they still use the Warp to do it, though they skim over it rather than diving through), and they know what psykers are from the Nicassar, so they'd probably try and recruit psykers and begin their own training programs. Lot of trial and error, but they'd find a way to get it fairly effective, eventually, without resorting to brutality as harsh as the Imperium. Probably sterilize any psykers they found, though, and take them whether they wanted to be taken or not, but after that part, a little different than the Imperium. Plus they'd probably do it in a gentler way. Might eventually just give up on them as being too risky to use, though.
But yeah, Chaos would be quelled when it was seen, and the populace would probably be educated and taught about the dangers and appropriate reactions, rather than simply told to hate. This could go well, or badly. Depends.
Finally, there doesn't need to be, and in my opinion shouldn't be, more disagreements within the main Empire. The Farsight Enclaves already exist, and the Third Sphere Expansion bringing the Tau in contact with them(they're the faction of Tau that 'grew up' as you put it) and the subsequent conflict between them should be enough. Other splinter factions might exist(I have a private setting in which the Tau sent seed ships to start other 'spheres' to colonize distant places and eventually meet with the main Empire again; only one of them lasted to 'present day' and they're rather desparately trying to carve a path back to avoid being overwhelmed) that have disagreements with the Ethereals or the like, but a. Ethereals settle their disagreements with duels, that's what Honor Blades are all about, and B. their hold is simply too strong in the main empire.
Also, the entire reason I like the Tau, beyond having realistic battle tactics, is their ideology. That while sometimes awful things must be done for the Greater Good, there is usually a third option other than 'adopt cruel policies' and 'let the empire crumble', as long as you're willing to look for it. So having them grow up and become just as grimdark as everyone else ruins the entire point of them.
Besides which, them being the naive race adds to the grimdark in it's own way; in the real world they'd be hated and despised for being inhumane and relentless, in addition to being propaganda-mongers, but in 40k they're the nice guys and wide-eyed idealists. The very fact that they're like children with pistols playing in a room full of serial molesters and eldritch horrors without realizing it is meant to give a sense of scale and perspective for the whole thing, a stepping stone so you can once again realise just how fucked up the galaxy is.