If I have only one hero active (others incapped, no hero targets in play), does the remaining hero get hit by something like Ermine's end of turn effect "deals the hero target with second lowest hp 2 melee damage" or some another similar effect?
If there is one hero target then there is no valid target in that case that is second lowest.
What about Plague Rat's Ravage, Vicious Onslaught, and Tooth and Claw when there is only one hero target?
You are considered highest and lowest health hero at this point so the remaining hero would get hit by all of those. In the case of Tooth and Claw they would get hit twice.
If 2 targets are tied for lowest hp, is one of them (player choice?) considered second lowest?
If there is an effect that deals damage to "the 2 targets with lowest hp" are both those targets affected?
Yes. If you had a card like that you pick the target with the lowest health and the target with the next lowest health before damage is dealt.