Minecraft – Why are some mobs 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.

Mobs cannot spawn in a well lit area, but only a single square is enough to allow spawning. The light level must be 8 or higher to prevent spawning, meaning no cube can be more than 7 steps from a torch. You have to count vertical steps too, so a torch two squares off the floor can only be five horizontal steps from any floor square.

In addition, spiders can climb up walls, and thus are harder to keep out than other mobs. But the fact that you have creepers and zombies as well indicates that you have a lighting issue. Creeps can also fall down from heights farther than they would choose to walk; if the cliff above your balcony can spawn mobs, you may wish to light it or fence it to prevent mobs from pushing each other off the edge and falling to your balcony.

After you posted the screenshots, I made this graphic, illustrating some of the squares that have insufficient light. The green dot means that area is light level 8 or higher (within 7 cubes of a torch). A red dot indicates it is light level 7 or lower, and mobs can spawn there. As you can see, there is a large splotch of darkness on the right side of your balcony, where it is widest. Add a few more torches and everything should be fine. I did miscount a bit when creating the graphic: the leftmost two red dots should be green, as they are 7 cubes from the torch that is just out of sight on the bottom left. This leaves 5 squares visible in the image that are below light level 8.