4k is a brutally effective move; if you're not using it often you're not using Mila right, I think. It's far better than 3k and honestly I don't think 4f+k has anything going for it other than a very tiny bit of range. (Edit: Ok, 4f+k has some very good uses insofar as it guarantees a critical state, which is useful online in particular since trying to do 4k shit on reaction is still pretty difficult; even offline, being able to 4f+k to 9k to p+k to ground throw is a useful way to get into mount quickly. Also, it's excellent combo filler after p+k or 1p+k/takedown cancel p, just fast enough to keep the critical going and just enough stun for 6p+k to work on fast stagger escape).
On block, 4k takedown should stuff almost any high or mid, takedown p should interrupt strikes, and takedown cancel should be almost entirely safe. I think takedown cancel k should interrupt a lot of things too, I'm not 100% on what it will or won't stop. As far as I can tell the opponent's only real option select out of this is a low OH, since I think that will technically stuff both the takedown and the cancel p, but I think the cancel k will beat that, need to check. Or you can just let it ride, you're only at -2.
On hit, you're at +2, so lots of options there. On counter hit, you've got a number of options outlined in the "takedown cancels from stun" thread (briefly, safely attempt takedown, cancel takedown and end up at +15 for pp or 6p or throw, or cancel takedown into p/k/2p), and a few others besides: 9k will hit if you input it immediately against a fast stagger escape (it looks like it hits in the last active frame hre so it's more like 19 frames in this application, hence the need for immediate inputs), but the distance may screw up a followup p+k to ground throw, so p6p6p may be best here. 6p+k will also connect against a fast stagger escape, giving you a nifty stun or the CB, if you've reached threshold. I need to try 4h+k from here to see if that gives a good mid kick option since nothing else she has will really reach from a 4k hit except 66k. I do hope the netcode is as improved as people say considering all this goes to hell in the lag. Especially the cancel game, since you can't really mash a throw out without getting a cancel p. Forget getting a 6p. (Edit: still goes to hell in the lag it seems like. Sigh.)
Also, in theory I think I'm warming up to 8ppp; first two hits are a natural combo and there's really nothing you can do fancy after that except to complete the combo (+6 on fast stagger escape). But that's kind of nice in that it's a shit or get off the pot moment for the opponent; either hold instantly or don't hold at all. Or buffer your hold trying to get the second p and eat a counter launcher or high counter throw. That works too.