"The damage a Pokemon can take until it faints"
I always thought this is HP.
"the damage it deals per second with a specific move"
TrueDPS
"I don't like the True-DPS-adjustment to defending pokemons defense stat, as this stat depends on defender, not on attacker"
Of course it depends on the defender. The attackers defense has no influence on the damage he/she deals.
Your EH sounds like it should be HP but it isn't. The def stat has no linear realation with HP. The def stat has an influence on the damage your mon is taken.
Maybe this helps you, if you want to develop a formula for the time it takes to kill an enemy.
http://pokemongo.gamepress.gg/q-a/new-highest-truedps-type