1. Electrically speaking, what is the function of the ground wires in the headphone? could a headphone work if those wires are not connected inside?
The function of the ground wires is to return the signal back to the source device (headphone amp, mp3 player, laptop, phone, etc) without a ground wire connection, the electrical circuit is not complete so electricity cannot travel.
The path would effectively be broken.
2. A bigger drive is necessarily more optimal in sound terms than a smaller drive? if we take the two drives of my previous pic for example, would that apply?
In my experience, the driver on the left looks more modern and I can only GUESS that it should sound better than the one on the right, which looks older and less capable.
Unfortunately, it's more complicated than that, since the driver is only a small part in the equation of how a headphone will sound.
• Earpads: Shape, size, depth, materials, etc will change how a headphone sounds.
• Enclosure: Open, closed, size, shape, material, acoustic damping will change how it sounds.
• Baffle: (the part the driver sits on) - material, density, venting and damping help tune the air-flow and sound of the driver.
Also larger drivers need more special consideration in design to prevent distortions from occurring over such a large 'inactive' surface area.
Dynamic drivers rely on a single thin area (the voice coil) as the 'motor' of the diaphragm, so most of the diaphragm surface is passive.
We can assume that the 'active' area of the diaphragm (the part that connects to the voice coil) is the most accurate and free from distortions, and the passive areas are more susceptible to distorting and affecting the sound - which can increase as the surface area increases.
However, larger dynamic drivers are usually more able to produce very low sub-bass frequencies as they push a larger surface area of air.
Planar-type drivers are generally larger than dynamic drivers, but since they're driven and controlled over almost the entire surface of the diaphragm, they can be MUCH larger without suffering distortions.
However, they need just as careful attention to ear pad, baffle, damping and enclosure tuning.
There are even more variables than this, and we could go on forever talking about them, so take the above with a MASSIVE pinch of salt and a gross-over-simplification
3. If I want to change a headphone cable, where can I find new substitutes? are they available at sound or electronic stores? if not, can I use cables from other devices?
You can easily use cables from other headphones (thank you captain obvious) but generally headphone cables are more 'specialty' and are not commonly found in electronic stores.
Most hobbyists use microphone cables since they can come with 4-cores, but often they're too thick and heavy to be useful for headphone, and are often stripped and re-sheathed with fabric alternatives like para-cord.
Maybe you should check out the "DIY cables" thread in the DIY section of the forum - lots of cool stuff there.
