Is this why kings could lead their armies in battle and survive?

That has more to do with the mechanics of combat than anything. Most casualties in pre-gunpowder warfare take place not during the fighting, but during the pursuit after one side breaks and routs. I've got some links on this matter, let me know if you want them.

Is it true that soldiers tried NOT to kill opposing nobles in battle during the Hundred Years War?

Yes. That's because a captured noble is worth more alive than dead. Have you encountered the phrase 'a king's ransom'? These following posts expand on ransom:

• u/MI13 has an excellent overview on the matter, and don't overlook the discussion in the comments - that thread's a goldmine;
• u/Lhyon outlines the general process of ransom;
• and u/The_Truthkeeper examines one specific case of a French knight captured at Agincourt, and how the arrangements were made for him.

More links in next post because argh tag limit.