Electronic – Simple switch with optoisolator – CTR related

For the grounding it's easy. Basically a switch can have not 2 but 3 state. Basically

• High when pressed
• Undefined when unpressed and not grounded
• Low when unpressed and ground

^{simulate this circuit – Schematic created using CircuitLab}

Grounding it will allow you to make sure the output low, without that it's a short circuit. So basically you'll use a pull-up or pull-down resistor for that.

They are connected in parallel means they are not connected one after each other but side to side. Example

^{simulate this circuit}

So from what I read in your question, the switch sound like a "master switch" who can act on both of the 3 other switch. If pressed, it's like all the switch are pressed. But hard to tell without precise schematics.

Adding R2 ensures that the base is biased firmly to turn the transistor off when the input is floating. Some transistors may leak collector-emitter current when the base is floating, some may not - transistors vary in characteristics quite a lot from device to device so it is wise to design your circuits with these large variations in mind. Assume you have the device with the worst characteristics in the datasheet, making sure you interpret the datasheet correctly when you do that.

In light of that, stability is referring to the stability of every circuit, be it made once or manufactured by the million. Keeping your circuit away from boundaries that can cause individual circuit behaviour to vary is a fundamental of design.