Explorer Medal maps

I believe that the "Cave of Life - Entrance" isn't the cave of life itself, but the map before it with the Cornian NPC, which pretty much everyone can enter, as long as they have enough HP/Dark Sight. It wouldn't make any sense if you had to be able to HTPQ (which would mean you're in the 4th job already, which means you already have the 4th job medal) to get a medal worse than the 4th job medal. On the other hand, this is Nexon I'm talking about but it won't hurt to try.

You do need to enter the cave by completing the pre-HT quest.

I believe you mean Victoria and Ossyria. At least that's what it says in the medal UI. I don't think I'll drop any of the medals unless someone can confirm that the medal count doesn't go down.

The count does not go down. I dropped 12 of my 14 medals and my count is still 14.