Hi,

1) the move states:
   Your animal companion is trained to fight humanoids. Choose as many additional trainings as its cunning.
Then -
When you work with your animal companion on something it’s trained in…
and you do something as indicated in the list, you add bonuses as written.
SO: the ranger descrives his move (as always), stating how he works with his companion, then he rolls (or takes damage) adding the relevant bonus.
Scouting the dungeon may be Defy Danger or Track, but the ranger must partecipate. HAving the druid to translate is so funny!! I wouldn't even require a roll.

2) you subrtact the ARMOR value from the damage you take. A hit having the "Piercing X" tag, counts armor as X points lower. You don't permanently make armor less effective. You treat it as X lower for THAT hit. A shield gives its bonus, period. BUT, if it'd be fictionally impossible or illogical, you could discard the bonus. The GM doesn'r rule this out. The fiction does.

3) Combat should take any amount of time as not to be boring, or useless. There's no fixed amount of time. Keep in mind that if it's your first game, you take a bit to get used. It's quite common.
As for Defy Danger, THE PLAYER describes what he does, then, if it triggers a move, that's it.

Player: "I move fast through blows, dodgind like wind, to do[...]"
GM: "Ok, sounds like a DEX Defy Danger."

4) If the damage come from a hard move, there'sno usually means to avoid it. If It's a soft move, AND the defending player CAN act, he can choose to intervene in the conversation, saying "I step in between and raise my weapon!". That would be good for me.

5) GM" The enemy shoot at you, arrows coming as rain; WHAT DO YOU DO?".
Say, the players state that they scramble somewhere, it could be a Defy Danger. If they roll a 7-9, the GM OFFERS a series of bad things, as per the rule. The enemy being closer is a valid option.

Players roll WHEN they trigger a move. If the move says they take damage, that's it.

The GM is not committed to play step by step. If someone fails, you say the enemy hits you. Take damage. Or, the enemy misses, but it's closer, now it'has a clearer shot.
And always: "Wat do you do?"

Remember, DON'T call for rolls. THE MOVES trigger the rolls, not the GM.

You don't normally check defy danger against damage. If damage is the direct consequence of a move (Gm or player move), it can't be avoided. That is, if a move says you take damage, that's it. If a (generally soft) move says you're about to take damage, and the GM asks what do you do, you describe what you do to avoid damage; if that qualifies as "Defy Danger", you roll.
There are no "checks" in Dungeon World.

Hi, dont' worry.
First, a PC can have more than one debility, as long as it makes sense in the fiction.

As for the other issues, it's important to tell the players to DO THINGS, instead of calling for rolls. If the thing they want to do is covered by a move, then make a move.
If not, is it a thing anybody can do? Automatic. Otherwise, Not possible!

So, a shield bash may be a defy danger (the danger is the enemy who bashes you back), or a hack and slash (doing the Paladin's Damage die); or you can create a custom move to apply when fighting CERTAIN enemies.

Discern Realities is rolled when you thoroughly investigate a situation, so:
1) just "listening" isn't enough to call for a roll.
2) the questions are appropriate as investigation results.

How do you resolve this? Some things, you can just tell them, using your principles.
Some things, can't be found out, if they come as GM moves. Or if they haven't got a thief.

Remember that you make moves when PC fail a move, or when there's a lull in the action.

You're with me, right? No "official" way, so you can really expand on the fiction, posing the question in the most "efficient" way, ok?

This is another short (but very useful) thread about the same topic:

http://apocalypse-world.com/forums/index.php?topic=6243.msg26461#msg26461

Hm... Not sure if this gets funded before noon.

Ah, yeah. In my country, it's 10.20 AM.

Grrr! More patience, next time, Uzio...
Bought all of them separately, except the D. Hero!

At the very least, you gentlemen could repay my fidelity by giving some leaks about this misterious Inverse World...

...And a teaspoon of Alchemical Exalted, which gives it a salty, metallic taste.
Not quite Dungeon World - like; more...Inverse feel.
Also, no alignment? Drives? The alignment part is slowly and steadily disappearing fron the sheets. What sort of conspiracy?!?
Seriously,
I find this is very colorful, well made, and not too complicated. This is hoe I see it:
you thought of it as another mission-oriented character, like the paladin, right?
You choose a course of action at the beginning, Sparatucs, Ulysses, etc, and take up the best matching moves.
Given the breadth of choice, this is by no means a problem.
Not for all campaign, I say; but in these days, a lot of altered-background settings are being created, so let's go for it!