Minecraft 1.10.2 Chest disappearing

As Ben Blank said, the only thing that will spontaneously cause an explosion, if you haven't made any TNT, is a creeper that got into your house. I see three possible directions for the creeper to enter from:

1. The caves

   Most likely, either you have an insufficiently lit patch of floor in the connected caves (walls and ceilings don't matter), or there is a dark branch that you haven't found. I strongly recommend always installing doors at connections between caves and living space.

2. The front door

   The damage you described seems to be focused around the doorward side of you. You say you removed "the bricks leading up to the door", but if there is still a one-block-jump path it is possible a creeper got in anyway. Next time, don't worry about removing the path, just close the door! If you have a wooden door, zombies can break them - this will cause a loud sound of someone punching some wood.

3. The ceiling

   You haven't said anything about your ceiling design. Is it possible that your ceiling had a hole in it through which a creeper entered? There are [minimal spoilers] ways for dirt/grass blocks to go away, so if you had a dirt roof perhaps a creeper fell in.

Miscellany

To my surprise, it appeared that nearly all my objects were still there. Most were sitting in the same spot that their chest was in. As best I can tell, I was able to recover nearly everything, with the exception of the signs and 2 of the 5 chest blocks.

Chests drop their contents when destroyed, as you saw. If there had been two explosions, then the second one would have destroyed all of your resources, as they have almost no “health”.

They also tend to leave big craters, and there seemed to be too little structural damage in this case.

The size of an explosion crater depends on the strength of the materials. If you meet a creeper outside, then it will leave a large hole in the dirt, but the same explosion will do much less damage to stone.

Oddly, the door and torches outside were gone, but the structure itself was untouched save for two holes in the floor (marked "Gone" in the above picture).

Wooden objects are generally weaker against explosions, and torches have no blast resistance at all.

Ahh, I know what happened. The lava has a new sound effect (it has been in there for a bit but it is overall somewhat new if you have not been playing for a bit).

Most people mistake it -exactly- for what you did, the sound of a slime hopping around as opposed to the sound of the lava bubbling.

As far as sound transmission goes, obsidian is the same as any other block and does not hinder sound (Sound only falls off based on distance to its source). But to answer the question of how did you end up at lava while tracking a slime, you were actually tracking the lava bubbling SFX.