I'm not sure I can answer all your questions, and I'm not sure I understand all of your existing setup.
It looks like your dual motors on the Y axis are simply 2 stepper drivers wired in parallel to a single motor axis on the Sound Logic board. Is that correct? This means that you are not able to move the motors independently to "square" the axis.
I don't understand why the touch plate board looks to have a significant power supply on board (and in fact looks to be ALL power supply).
And the "board on deck" looks like a different board than the "main board" and is wired to more stepper motors????? Are you running 2 parallel ports?
The "main board" looks like it has 3 outputs driving something. Do you know what these are?
That said, if you are happy with having the 2 gantry (Y) motors driven from a single set of step/dir signals, then I believe PMDX-126/107 combo will work fine with your existing PC and Mach3 setup.
Staying with Mach3 or upgrading to Mach4 is a tricky question. If Mach3 does all that you need it to, AND if you can continue to run on an older Win OS that supports Mach3 (I think that means WinXP or maybe Win7 but I' not sure), and as long as your PC has a physical parallel port, then you could stay with Mach3.
Mach4 is the newer product, and is actively being supported and enhanced. Mach3 is what it is and there will be no further updates. Mach4 adds some nice features, but if you are happy with Mach3 they may not be of any advantage. More easily customizable screend and easier scripting language are two noticeable ones off the top of my head.
However, if you intend to get a new PC, that new PC will likely run Win10. This means Mach3 won't work on Win10 and Mach4's parallel port driver won't work either (it is 32-bit OS only, which means 32-bit Win7, XP or Vista). And the new PC will likely not have a physical parallel port. In that case, if you already bought the PMX-126/107 combo, then, yes, the PMDX-411 will work with Mach4 and your PMDX-126/107. Your Mach3 config may need a few minor changes to work with the PMDX boards, but I wouldn't expect major changes (well, maybe with spindle config).
Though if you intend to get a new PC sooner rather than later, you might consider skipping the PMX-126/107 and going straight to something like a PMDX-425 and PMX-407, or a PMDX-416 and PMDX-407. This also means Mach4. So this would be an entirely new PC, Windows version, Mach4 environment and breakout board. Maybe a lot to tackle at once.