So they are hypothetical answers to problems being suggested by the math? What is the confidence level that we're understanding the math and that these theories are even likely?
Well they all fit the math. The problem is there is not enough that we know to completely flesh out the hypothesis. When you add to the fact that these concepts are not even testable yet adds further chaos. Testing is what verifies the math. When you can't test, you don't really have anything.
Why can't we test? What is stopping us from figuring out how to interact with parallel universe? If it isn't possible, why?
The simplest answer is, we don't know how. Don't forget, we just proved the Higgs Boson. And we had to build a GIGANTIC particle collider to do it. And what did we find out? More questions. The Standard Model calculated that the Higgs should be at energy level A. String Theory says level C. The LHC found it a level B. Right in between the two theories. Saying this is an ongoing process would be an understatement. It's also what makes it the most exciting IMHO.
Just to take you up on your comment about the Higgs bosons, what you say is not really correct. Firstly, as far as I am aware, the mass of the Higgs boson is completely compatible with predictions from the standard model. Secondly, I don't think string theory has any predictions to make about physics at energy scales being tested by the LHC, and certainly didn't have any concrete predictions for the mass of the Higgs (after all, one of the main problems of string theory is that there are many string theories and we have no idea which is the correct one, if indeed one is correct). Thirdly saying The Standard Model calculated that the Higgs should be at energy level A
is not really true. In the Standard Model, the various parameters (such as "bare" masses of the particles and "bare" interaction strengths) are input parameters which one plugs in by hand; there is no calculation directly of the masses (although one can compute corrections to the "bare" masses due to interaction in terms of the input parameters). What one can do is vary, say, the mass of the Higgs and see if one gets computed quantities compatible with the observation; it doesn't directly "calculate" the mass (sorry if this is a bit pedantic).
That's interesting. Do you have any links to youtube videos on the topic?
Check out a documentary called Particle Fever it chronicles the discovery of the Higgs.