Reading over the mini-dex I like quite a few of the concepts. Most of the items and abilities being pulled from actual resources is a nice touch and gives a reference point on why its there, some people may complain but going back to the original source on how that legion operated is a good way to start. However many of the abilities need to be updated to the current edition to provide a more balanced game (for both sides). Some abilities were too weak while others were incredibly strong.
Let me go down a quick list of some things that stick out to me...
Alpha Legion
I like your setup with these guys except the fact that you are required to take the more expensive troops at the same cost as Chosen. I say make this an optional upgrade so you don't end up wasting points for not outflanking with chaos marines with a rhino.
Iron Warriors
Update the Basilisk to the current IG version (Smaller min range) and correct the armor typos. I know in the older Iron Warriors you could "give up" 2 fast attack slots to gain an extra Heavy Support but 9 oblits are bad enough I rather not see 12 of them! Maybe if there was a limit on what you could take in that situation it would be alright. I like the rest of their stuff you have for them through so great there.
Night Lords
Almost perfect, I'm surprised they don't have Night Vision standard and you already said you fixed the way their cover bonus works. One thing I would be wary about is giving raptor troops Hit and Run, giving a scoring unit a way to escape close combat can be extremely powerful if used right and maybe you should only allow Raptors taken as fast attack choices to have this ability.
Word Bearers
My only issue was already bought up by an other poster and you said you have taken care of it already. So they're great so moving on!
World Eaters
Raptors being added is a good call but personal I don't think Havocs (or Oblits for that matter) belong in a World Eater's army. Its all about ripping apart the enemy and not caring about those silly things called "tactics" or "strategy". The rest of the upgrades listed make up much of the lost of these units. World Eaters are supposed to be close combat monsters, keep them that way. :P
Death Guard
You already taken care of the Plague Carrier so that takes out my biggest issue. About the Rhinos, in the older codex they were allowed to have two rhinos included in their troop choices and then the rest counted as fast attack. However other sources since then removed that rule so it can vary. Troops having no access to rhinos is a problem in 5th edition. However, you can also be cheap and keep them as fast choices but have them still count as scoring units (Similar to how Sternguard Vets are scoring units for Crimson Fists). Random thinking there so feel free to count that pointless rabble :P
Emperor's Children
The main problem with these guys is their over priced guns, but they were always badly priced so I don't really hold it on you there. However Doom Sirens are more priced towards Meltas or even plasma guns depending on which source you use, being the same price as a flamer is a little iffy. Also BlastMasters were the same cost a Lascannon (or just slighty higher). I would also remove warp scream ability as you are already I5 and having to do leadership test all the time for no reason just slows things down for no real reason. Like others have said, add the raptors back in.
Thousand Sons
Issue taken care of already. They look good to me!
Chaos Undivided and Minor Psychic Powers
I get the point that you want to add some of this stuff just because however it doesn't really fit into the whole concept of your mini-dex. Plus these may mistakenly open up more cans of worms that what might not be intended, I would put these on hold for time being or have restrictions to only certain legions can take them.
Suggestions
While Minor Psychic Powers aren't part of the game any more, some of them may be fine to make into full fledged psychic powers you could add into the various legions. Giving them more than just one special psychic power per chaos god. An other thing I think you can possibly go into is a way to make possessed more unique to each of the 4 pure legions as a World Eater's Possessed should be greatly different than those of the Emperor's Children.
Overall I like what you have and you get most of your points across. There is a bit of picking and balancing to do but thats always the case. Keep in mind there will ALWAYS be arguing over what is "fluffy" and chapter X should have access to everything possible with no drawbacks. Its obvious that you loved the old codex and want to "update" it to fit into the 5th edition world and its coming along very well, so don't let people "force" you to change the fluff so you can make them happy. I can't wait for you to release the next version and keep up the good work.