Diablo – Bounty Rewards Increase by Torment

Each difficulty level has it's own crafting materials. For example, in Nightmare Mode, Subtle Essence is replaced by Shimmering Essence, and Fallen Teeth is replaced by Lizard Eyes.

Once you start needing drops from a higher difficulty to train your smith in higher levels, you can know that you won't be able to craft anything learned at those higher levels without materials from those higher difficulties.

So, in short, No, there's no real benefit to doing this. You can also browse all of the crafting recipes, sorted by Smithing level over at Blizzards Game Guide site. As you can see, Level 5 Crafted items learned via training require level 30 or above, at which point, you should be in Nightmare mode. If you're learning these recipes while you're still in Normal Mode Act II, you're either severely overleveled, or you're already at a point where you can craft things long before you're able to use them.

It is possible, but no, nothing interesting happens.

I completed all the slabs on my last run through this dungeon (Hell difficulty), and absolutely nothing happened other than the mobs that spawn when you step on a new slab.

Partway through, I managed to get to the far corner, where there was a Resplendent Chest waiting for me, but it definitely was there well before all of the tiles were filled in.