I was holding an iron pickaxe and accidentally left clicked on a DHD that generated in the village I was in, and immediately crashed.

Crash Log

This might be caused by one of the other mods I have (FoamFix and VanillaFix are likely culprits, as they mess with rendering stuff).

Also, what level pickaxe is required to mine a DHD? TOP always shows that they are not harvestable, even when holding a Diamond pickaxe.

I encountered this same bug - the culprit in my case was VanillaFix. I'm sure you've since figured something out, but in case you haven't, I had to disable the textureFixes portion of VanillaFix, unfortunately.

I can't even look at the line in TextureMap that caused the NPE because your client is using something to inject nearly 1,000 lines of code into it.