Minecraft – What’s the maximum height mobs can fall from without dying

Actually, their jumping up and down helps, I think — assuming you're using the “idle to collect a lot of mobs, then kill them all” strategy.

In my skeleton-punching endeavors, I have found that, as best I can tell, dead bodies absorb hits. If I have mobs trapped in one spot and I hit in the same direction repeatedly, then only one or two will die, then nothing happens until the bodies vanish.

Therefore, if they are jumping, some of them will pop up while dying, allowing you to get more hits in. In fact, to further improve matters, I've widened my skeleton holding pen to 2 blocks wide so that I can alternately hit one side and then the other. (This picture shows only two skeletons because I just walked over to take it; ordinarily there would be a lot more, and some of them will constantly hop between the two open blocks.)

On the other hand, if you really want to stop them from jumping, such as if you only have one or two at a time, then here's some ideas:

• From the drop, let them wander into a water current which then moves them horizontally into your holding area under a two-block ceiling.
• Place a cobweb block above their heads.
• Place a trapdoor above their heads, and toggle it open periodically (with a redstone clock) to let new mobs in. These two ideas will interfere with the fall damage.

The renewable resource page on the Minecraft Wiki is a great help.

I did something like this on an adventure map ("Land Claster" or something like that) where you're thrown onto a floating island and there are a half dozen others you can build towards. I might recommend a pre-made adventure map like this so you can learn by experience.

As far as what you need to build stuff versus living in a cave; the easiest renewable building material is wood. You need dirt to grow it, but you never consume it. Metals, strictly speaking, are renewable, but you can only get gold from Zombie Pigmen (in the nether), and iron from killing (personally, mob grinders don't work unless they just weaken them) Zombies. In order to get into the nether to get gold you'll need lava, water and diamond (or loose blocks of obsidian). Lava and water can also be combined in a cobblestone generator to create infinite amounts of stone (using a slightly less infinite amount of wood).

Animals yes, and you'll want some grass to feed the sheep and be able to use bone-meal to force some tall grass to get wheat seeds or flowers. Bone meal is free; almost too easy in a sky map with limited spawn space; you'll be rolling in it once you get a grinder going, along with tons of absolutely useless gunpowder.

Sand/glass is another non-renewable resource, along with other minerals; gravel, redstone, lapis lazuli, etc. "Coal" proper isn't renewable, but you can make the next best thing; charcoal, endlessly with your tree farm.