Too many questions for one reply close to bedtime. I'll take a stab at the easiest one. Don't have the focus to write sufficiently precisely about quantum corrections to the Higgs vev while half awake without a grave risk of flubbing it. I would be stunned/flabbergasted and highly skeptical. Why? Even if SUSY particles or Extra Dimensions do exist, they almost certainly can't be "just around the corner" such that they could appear clearly at the LHC in the near future. Those phenomena would pretty much have to start giving rise to experimental hints of their existence orders of magnitude before they were observed directly because there are multiple observables in HEP that are sensitive to physics at much higher energy scales. While the direct exclusions on phenomena like these are in the low single digit TeV zone right now at the LHC, the indirect probes of higher energy scales pretty strongly disfavor this kind of phenomena much below 10 TeV. At best, you might can an inconclusive glimpse of it towards the end of Run 2. What you would expect instead is a mosaic of correlated deviations from SM predictions in multiple channels. For example, if SUSY exists, we should be able to experimentally observe material differences between the SM beta functions and the running of the SM coupling constants that are observed long before we can actually discover a new SUSY particle. Anomalous magnetic moments are also a pretty powerful indirect probe of high energy scale physics. Still, if that did happen, obviously I'd have to recalibrate my expectations just as physicists did decades ago when the muon suddenly appeared unheralded and unexpected, when SR and GR fundamentally altered our understandings of time, matter and energy, when the singularities predicted by GR turned out to be physically meaningful (even if they turn out not to be true classical singularities) instead of merely mathematical pathologies of the theory, when scientists discovered that quantum physics is inherently stochastic. It would dramatically change the entire field. Probably the best prospects out there right now for new physics are the multiple experimental hints of lepton flavor non-universality in interactions involving charged leptons. But, that particular example is tainted by the fact that other experiments in which any reasonable kind of lepton flavor non-universality that really exists should also manifest place extremely tight bounds on that possibility. It is extremely hard to come up with a sensible way to distinguish experiments that hint at non-universality from those that rule it out strictly in any plausible way. If the LHC or some other experiments do see BSM physics, it is more likely to be something that hasn't been analyzed to death by theorists because our currently event cuts, experimental designs, etc. are specifically calibrated to be as sensitive to those theories as possible and have, so far, come up with nothing. Some of the phenomena I think we might be more likely to stumble into more or less unexpectedly would include: 1. A new boson that mediates neutrino oscillation. 2. Definitive proof that space-time is not perfectly smooth and continuous and instead has quanta scale non-localities. 3. A gravity modification arising from an effort to develop a quantum gravity theory that explains most or all dark matter phenomena and at least some dark energy/cosmological constant phenomena. Put another way, I expect the biggest deviations from GR in a quantum gravity theory to be in the weak fields and not in the strong fields. 4. Extremely rare and short lived top quark hadrons. 5. Inconclusive early indications of a composite nature for one or more "fundamental" particles of the SM that overcomes previous "no go" evidence with a novel loophole of some kind. 6. A new unpredicted phase or state of matter analogous to Bose-Einstein condensate or quark-gluon plasma that emerges in some characteristic boundary conditions with surprising new properties.