Dear Cantab Morgan, I admit I could have been confusing. I was trying to give a quick and moreover the most straightforward and intuitive answer to youngsters (since wing81 is more concerned with didactics), but as a matter of fact I realize in this case relativity is somehow misleading...
Hello. The first definition is tautological and cannot give any additional info! The second definition is fine. Remind this, too: kinetic + potential = mechanical = energy that is conserved in presence of conservative forces.
Thermal energy is ultimatively kinetic energy. With nuclear energy...
Hello. To give a young student a very simple and intuitive answer, I would just let him imagine a free particle. You can ideally give it more and more KE but since it cannot overcome the speed of light, there you get an upper limit.
Is that in line with your ideas in terms of explanations...