But apart from this, I don't know what could have gone wrong in this scenario
The 3 pin connector was not connected and I'm here wondering if maybe there were a problem in the connector itself, creating a short circuit ?
your breadboard tracks trying to carrying over 1A
Can I ommit the capacitor if I want to power 100 LEDs (needing 6 amp exactly) ?
Does it means that breadboard tracks has an Amperage limit ? I don't know anything about this
I guess that amperage difference would bright up leds yellow when too far away (as I've read across forums ?)
You need to understand what the capacitor does. It smooths the voltage in the face of rapidly changing current demand. With the sort of current you have you need one. The power supply will not cope with that much ripple.
Actually, the power supply will cope with that much ripple.