Oh man, these aren't quickie answer questions... but...
... I'll make 'em quick (for now).
- Some of these features have been around for years, some now just cropping up on "radar packages"... most are good descriptors of what's going on but should not be used to make decisions per se. It's more during/after the fact. Plus, you can easily have a tornado (especially a weak one) without some of these factors.
- One more quick context: for several decades, but especially the last 15 or so, one "breakthrough" that seems to have occurred with understanding tornadoes is that sorta somehow, a wind "gets going" on the surface, a circular type of thing, kind of like a "sideways tornado" only the wind isn't (yet) nearly as fast. That "sideways wind" gets picked up in a supercell as updrafts increase (i.e. air going up into the cell and becoming vertical). Then that air cools as it rises, gets faster, and begets all kinds of hell (hail, electricity... and spinning vertically). So the idea is that a tornado usually (well, educated guess) develops when 2 factors are present, and usually both must be present - only one doesn't cut it. The factors are: 1) velocity of the column of air begins to show a great contrast (usually the upper part in mid-level atmosphere spins a lot faster than the lower part). And: 2) there needs to be sort of a continual 90° "bend" of horizontal inflow air, which gets pulled up, gets vertical, and spins faster. Again, this seems to be a reliable factor, but it's the tip of an otherwise non-really-well-understood deal. So what some of these values are, are measures of the strength of the differences in velocities through the air at lower levels (LLRV in the graphic above), maximum difference between velocities measured at various levels (MRV), and the greatest difference in the lowest clear level of rotation (LLDV). What all this boils down to is that tornadoes like 1) "bent" wind coils, and 2) different velocities (shear) up the column.
Basically this is akin to sabermetrics in baseball... a lot of newfangled measurements that might mean something significant... but might not. Fun stuff to play with, but not supposed to be at this point anyway the Ten Commandments of Tornado Formation.
So I'm gonna skip over the very long links between this idea and the metrics for the most part (lots of calculus there), so I'll just answer the others you named:
- Storm relative depth - this is a general number derived by calculating the distance between the storm's inflow (usually at or near ground level) and the height of the storm's most pronounced shear point (greatest difference in velocities in the column) within the lower levels of the storm (something called effective bulk shear, or EBS). These are complex calculations, with readouts that would stymie Einstein, but it's sort of boiled down here to the percentage of the column where these extremes take place; i.e. the distance is about 62% of this column in the lower part of the storm. It is not a simple measurement of the storm's height or whatever. The idea here is that the larger the % in this figure, the more likely a storm is to have tornadic potential - but again, it doesn't mean it'll happen.
- Strength index is again a fancy calculation of measured points in the lower level of the storm. The idea here is that it seems that storms that might go tornadic often have strong rotation, often the strongest in their lower levels (makes sense, a storm with higher speed rotation in the upper levels might not touch down and so there's no tornado). Storms with higher lower-level rotation get the higher number... so a storm with say 2,304 is going to be "less likely" to go tornadic as one with say 6,403. In this case, 4392 is about lower-mid severity on the scale. Storms with 6500 or above are most often associated with tornadoes.
- TVS signature - this is a 1/0 terminology determined by a bunch of calcs (duration, depth of shear/column, speed, etc. a figure that covers the speed of rain moving to/from the sample point, etc.) that all gets boiled down to a "true" or "false". However, again, 1) storms that show "true" might be rotating higher up, so it's not a given that it's going to be a touchdown, and 2) there have been tornadoes, especially weaker ones (EF0-2) that might not even have this signature because the vertical column of shear might be very shallow or so discombobulated that the signature hasn't shown up. You often see these signatures in the well-known "red/green -yin/yang" Doppler signatures air/rain moving toward the sample point shows up green, moving away red). Usually when you see that popping up, you tend to ignore the "true" or "false" determinations (it's right there before your eyes, though 99% of the time it'll be "true). This is more for less-developed shear storms. In this case it says that it's not (yet?) picking up the traditional to/from diversity in a rotating storm.
The calculations themselves are way out of my league, but I sort of understand what they mean. Good enough for now, I guess.