I was going to not really bother leaving a comment because I don't know what I'm talking about and the post is a bit old, but then I read the other comments and I feel like you should get one that's actually interacting with the concept.

So: I find the two-previous-references design fascinating. It seems like there's no reason that shouldn't be able to work in some design, and if you could make it do that it's way better than blocks. Also the proof-of-work aspect seems arbitrary; it could be done with proof-of-stake as well.

Whether it works seems like it would depend on a more rigorous resolution algorithm, though. I'm not sure probabilistic is necessarily a bad way to do things mathematically but I'm betting it would have results that make a lot of humans uncomfortable. 

>In IOTA, if the transaction volume suddenly drops, it appears that the network instantly becomes more vulnerable to attacks.

Sure, but in this system, and especially in the hypothetical proof-of-stake version of this system, it would be pretty easy to set up a "white knight" account which simply produces null transactions to keep the volume up. 

As for your five questions:

>Does a cryptocurrency need a blockchain, or is IOTA's "Tangle" just fine?

I don't know if IOTA's specific tangle is just fine or not, but I don't think there's any reason to require a distributed ledger to work in only one dimension. (Linear blocks.) In fact it seems like a pretty big weakness to me.

>What are the consequences of separating users from block producers? Does Bitcoin

Not sure what this question was supposed to be. Steem seems to work pretty well on the blockchain side of things, but I'm guessing there was more to it than that.

> What are the fundamental limitations to secure transaction rates?

Now that one's really interesting. I not only have no idea I have no approach.

>Are the IOTA Foundation's claims that "the network gets faster the more it is used" correct?

This seems anti-entropic? I guess maybe it's tied to the nominal PoW somehow. But I would think that a large part of the value of such a network is that it's close to maximally fast all the time. (I'm still thinking more about the PoS version.)

>Why do Graphene-based DPOS chains apparently perform so much better than PoW mining chains? Has something important been lost, or are they just better?

My understanding is that PoW mining chains make things arbitrarily difficult in order to restrict block production. There's no useful work being done in the PoW part of things. If you can restrict block production in other ways - by stake, by delegation, or by designing a system that doesn't require it - then all of that hash power is completely unnecessary.