1) How will the LEDs respond?
Since there's no resistor for LED2, it will illuminate fully and consume the whole power from the source, giving no chance to LED1 to illuminate.
2) A few 3.3 V LEDs are connected in parallel to a 3 V source. Assuming all the LEDs have identical specifications, how will the LEDs illuminate?
Since all the LEDs have similar specifications, all 3 LEDs will light up with uniform illumination.
3) A manufacturer has produced 1000s of the below given LED circuit, but he complains that strangely many units have shut down permanently after some use. However, there are also many of these units which are working normally? Please help him to solve the problem. The LEDs are 3.3V, 20 mA.
The resistor value is incorrect, which is causing the LEDs to work under stress and above the tolerable current limit. Therefore the weaker LEDs are gradually getting damaged and shutting down, while the stronger ones continue to sustain, but might eventually fail someday.
4) A white 3 V LED is connected directly with a 12 V supply, that looks dangerous, isn't it? What is your opinion?
The LED will illuminate safely, although with lower brightness due to an inefficient configuration. The LED is rated at 350 mA, therefore it will force the 12V/50mA to drop to 3.3V 50mA, and will illuminate using 50 mA current, and dimly.
5) In the below shown circuit since the total forward drop rating of the 4 LED string is 3.3 x 4 = 13.2 V, how will LEDs respond to the 12 V supply?
The LEDs will light up quite optimally using 3 V across each LED.
6) Which LED combination is the perfect one?
The left side circuit is better, but not the ideal one. The ideal circuit will have two parallel strings of LEDs, each having a 470 ohm in series! https://www.homemade-circuits.com/wp-content/uploads/2019/07/Q6a.png