what I'm seeing is pure lack of under hood maintenance from the pictures I'm seeing. Keeping the engine compartment at least half way clean prevents alot of problems.
Dirt attracts moisture which in turn will give voltage a path to flow. This includes across the top of the battery from terminal to terminal or terminal to hold down, or any path it can establish for that matter. the corrosion your seeing is actually created by small amounts of sulfuric acid (yes, they give off vapor occasionally. when this mixes with moisture it becomes acid again) from the battery mixing with the moisture in the dirt and being attracted to a voltage source.
the powder you are seeing is actually dried acid and is in itself caustic. don't brush it off and blow it away, you're just leaving it to create corrosion elsewhere later, or find it's way back to where it started.
either mix up some baking soda and water or grab a can of coke, either will neutralize sulphuric acid. gently pour on and you'll see it foam (I pour it over the entire battery and terminals and also the top of the tranny). let it do its thing for a bit, apply liberally once again and give a little time, when foaming quits rinse with fresh water and brush, or disassemble then reapply once more, then rinse and clean.
Keep your battery and surrounding area clean if you want it to keep you happy. as some have found, repairing battery cables isn;t cheap. but 20 minutes every 6 months or so can save a boatload of time and money. :)