Ok, you've got several things listed there, I'll try to clarify the areas for you.
a. That would be electromagnetism, since lightning is a mass transfer of electrons from the clouds to the ground. Electromagnetism deals with anything that's basically electronic or magnetic. Such as magnetic fields, circuits, lightning, static electricity, etc.
b. How energy is produced by the sun is a basically relativity and to a degree nuclear physics, the primary equation for mass to energy conversion is E = mc^2.
The following is a more detailed explanation for how energy is produced by the sun.
Stars do rely on the interactions of nuclei to produce energy. The type of nuclear interaction that stars generate is a fusion reaction. Stars are able to compress deuterium atoms together and create helium via a fusion reaction. The energy released is enormous, it can be calculated by e=mc^2. The mass that's converted to energy is somewhere along the lines of .07% of the total mass is converted to energy. Thus making it a very large source of energy. It couldn't be a complete conversion otherwise we'd have no elements and the sun would not exist.
A common misconception is that fusion takes hydrogen atoms and turns them into helium. The fusion reactions uses an isotope (element with a greater or lesser number of neutrons than the standard element on the periodic table) called deuterium or "heavy hydrogen" and slams those atoms together to create helium.
The reason it has to be deuterium is that normal hydrogen consists of 1 proton and 1 electron. Helium consists of 2 protons, 2 neutrons and 2 electrons. Deutrium which is an isotope of hydrogen contains 1 proton, 1 neutron, and 1 electron. Thus making it the only real candidate for fusing together to create helium.
I realize the answer is rather long, but it's the best one I could come up with.