I had a brief look, but need to look a little further into the references (I have over 400 papers). But in general, this is quite a challenging topic to get into.
This is one my favorite papers on failure criteria discussion:
Carl Q. Rousseau
A Range of Practical Failure Criteria for Laminated Composites
Reference: Rousseau, C. Q., "A Range of Practical Failure Criteria for Laminated Composites," Composite Materials: Testing and Design, Fourteenth Volume, ASTM STP 1436, C. E. Bakis, Ed., ASTM International, West Conshohocken, PA, 2003.
Tsai-Wu - In this paper the category labeled "Tsai-Wu" includes all lamina-level interactive, or polynomial curve-fit criteria. While possible to formulate these criteria for solid or beam-column stress states, the vast majority of the derivations and applications are specific to in-plane failure in states of plane stress or plane strain. Beyond the advantages and disadvantages listed in Table 4, it is important to put the development and use of this criterion in proper historical perspective. During the 1960's and 1970's the emphasis was on proper ways to homogenize both the elastic response and the failure physics of laminated advanced composites. Traditional approaches used on glass/epoxy structures in the 1950's were to simply assume that the mildly orthotropic glass/epoxy fabric laminates were isotropic, and use very conservative strength allowables without regard to lay-up. Since this approach was unacceptable for highly orthotropic boron/ and carbon/epoxy, and targeted applications were weight- and fracture-critical primary structure, the two most popular failure theories to emerge in the '60's and '70's were (a) stress-based interactive criteria such as Tsai-Wu, which attempted to capture all fiber and matrix failure modes in one failure index (in order to provide the analyst a work-load comparable to what they were accustomed to on isotropic material); and (b) translaminar fracture-based criteria which attempted to parallel the metallic state-of-the-art at that time in LEFM. Since the 1970's increasingly routine applications of carbon/epoxy advanced composites have lead practitioners to gradually become more concerned with (a) correctly separating and capturing the constituent-level failure physics (in lamina- or laminate-level failure criteria); and (b) applying criteria that are as simple and straightforward as possible, in order to ease allowables-development/application cost and regulatory oversight (i.e., explaining your analysis to the government). Thus, use of interactive criteria such as Tsai-Wu, given the disadvantage noted in Table 4, is on the wane.
The point there being is that in the 60's and 70's there was a lot of hope and guessing that these failure criterion would be true predictors. The truth is that it did not work out like that and we still not have a failure model to predict actual failure (though SIFT seems to be gaining popularity).
For item 2:
The major problem with lamina based failure criteria is that actual failure occurs at the laminate level. The complex state of 3D stress and psuedo-plastic type failure that actually occurs (holes and bolted joints), usually render pure lamina based failure criteria questionable. In addition, free edge delamination in unnotched specimens cannot be accounted for. In fact, when dealing with real failure modes for holes/bolts/impact, all of the lamina based failure criteria start to make less sense. At that point, one starts to consider test data and failure models such as W-N (point stress, etc.), which are semi-empirical and by definition cannot capture the actual failure state.
Like I said, this is quite a complex topic, but those are some general thoughts behind my comments. I also have a good graphic (which I can't locate immediately) which shows the use of the different failure criteria in industry. The max-strain is the most popular, mostly for the reasons Carl mentioned.
Brian