Hi there! Welcome!
As Jared notes, you need to make a number of Beginner’s Luck tests equal to your current maximum Nature. If you have Nature 5, you need to make 5 Beginner’s Luck tests before you learn the skill. When you learn the skill, it opens at 2. See Learning a New Skill on page 30.
(2) Can you always use Nature for skill checks, if you don’t have the skill?
I need to tweak Jared’s response here a bit. You can ALWAYS use Nature if you don’t have the skill, whether the action is within your Nature or not. The only caveat is that if something is against your Nature, your Nature is taxed by the margin of failure if you fail. See Nature on page 26. Pay special attention to the Acting Within Your Nature, Acting Against Your Nature and Taxing Nature subheads.
(3) Is there a way to get equipment that’s not on the list prior to the first adventure, i.e. a bow for the elf? No armor and only a dagger. Poor man.
Not by the rules as written. Don’t feel sorry for elves. Elves are extremely potent characters with many, many benefits. It won’t hurt them to have to buy or make a bow or armor in play. You can always house rule it, of course.
(4) The elf tended to the warrior’s injury with the heal skill during camp phase. The warrior was exhausted at that time. Did they have to take care of that before?
Characters need to Recover in order, but treatment is not Recovery. You can use Healer to treat someone’s injury no matter what conditions they have. Note that if you fail a Recovery test, you can still seek treatment. But if a Healer fails to treat you, Recovery is no longer possible. Instead, you must suck it up (See Treatment for Injury on page 77). If possible, it’s better to attempt Recovery first, since treatment is all or nothing. However, but the benefit of treatment, as you discovered, is that you don’t have to recover conditions like exhausted first.
(5) Moving from room to room seems pretty effortless. The group easily skimmed through the rooms. And I didn’t want any Cartographer rolls for only four rooms (they didn’t proceed beyond the secret door). It felt a little strange. A long time ago, when I played dungeon crawls before Torchbearer, time passed when the group moved around. Things (barred doors, traps, monsters) happened when the group moved around. In Torchbearer, things happen, when adventurers do stuff, i.e. skill rolls. Time doesn’t pass, when you move between rooms, unless there is something around. I know, I can throw in a wandering monster, when the movement becomes too effortless. Or I’d let them make cartographer checks, when the halls and corridors become more labyrinthine. But in such a small structure, I wait for the adventurers to dig their own grave while exploring the different features of the rooms. Less “move to encounter A, proceed to B, get to C…”, the players have to be more proactive. It feels different, and I think I like it more.
(No question, more of a musing, yet I’m interested if other people had a similar experience with Torchbearer.)
Yes, that’s pretty much how it works. Cartographer is something you test after you’ve explored for a bit and want to make a map of what you’ve explored.