Tune -> Bed Z
Per description in this table, this refers to the Mesh Bed Leveling process. It allows to modify all saved mesh z-offsets by the given amount.
Tune -> Babystep Z
This just instructs the motor to move the given amount, once, without changing any ...
Part of your self-answer:
What is puzzling is why did the 3D printer run as if the computer was still operating it, when is was printing from the SD card? Was the circuitry getting power from the USB cable from the computer?
is more of an extension of the question, which I'll answer. Generally, yes, the logic of many (most?) 3D printers can be powered by ...
So the new silicone buffers raised the bed by 5 mm? When this happens, you should raise the endstop also with 5 mm. Else the printer will go down to the Z endstop that is effectively 5 mm below the level of the bed. I guess the buffers cannot be compressed by 5 mm, so you need to move the endstop up to the level your buffer compression is in reach of.
The MKS Base v1.2 is basically an Arduino MEGA2560 and a RAMPS1.4 on a single board.
You can use the RAMPS pin designation.
Note that the endstop to origin distances is explained in question How to center my prints on the build platform? (Re-calibrate homing offset).
In Jims Marlin fork you can find this at:
#define X_MIN_POS 0 - XTRA_BED_LEFT
The issues you are facing can be caused typically by a defective X-axis endstop, an inverted logic of the X-axis endstop or a defective printer controller board.
When the X-axis endstop is reporting being triggered, it will not move. After "homing" it will only go to the right of the "home position".
There a couple of things to troubleshoot the X-axis ...