It appears water doesn't stop logs from catching fire, as they caught fire in all of these configurations (I lit the Netherrack blocks on fire for all the tests).
Water underneath:
Water on the sides:
Mixture of configuration 1 and 2:
Water flowing right to the logs:
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:
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.
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.
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.
Best Answer
Assuming you play this as a challenge - no other biomes, just surviving in the desert:
As of 1.9 dead bushes when broken drop sticks. This makes the challenge much easier than before.
Seek caves (may take some trial and error; some may be buried under the sand) and try to find an abandoned mine. There's wood aplenty in there, in the form of the supports. Some smart creeper management can earn you cobble and coal. Some village houses contain crafting benches you can then use to assemble stone tools without access to wood.
Edit:
Desert hell was a challenge stream of gameplay in a desert world, with no mineshafts, villages, and caverns. You may watch it for some very creative solutions: