So after sleeping it off, it gave me a chance to clear my head and brainstorm a few things. This is me just tossing a few ideas around. Feel free to throw in your two cents or whatever, but this thread more or less acts like a hub for me to get my ideas down somewhere so I don't flounder with them later on. Where to start where to start. Oh, it should go without saying, there will be spoilers all the way up to the most recent chapter of the manga. It will still be spoiler tagged, but just a friendly heads up. But just to be safe all my explanations are going to be in spoiler tags.
What's REALLY in the basement:
Motives of the fodder titans:
I agree with everything, except the basement part. I have no idea what could be there (there will be information, maybe a book, about how Titans appeared, but other than that...), but I don't think it is what you said.
I think what's in the basement isn't something physical like a brain or something. More like a map or papers (something small). His Dad seemed very certain on Eren keeping the key to it (surely if it's just the key to the door that's unnesesary? They could easily barge through it). Unless he has the key to remind of him of what to do.
As far as Titans go I think the "feeling empty" is on the right lines. Especially seeing as they don't try to eat animals so it can't just be a "primal desire". Either that or some kind of preprogramming to kill humans. The Beast Titan seems to suggest this as well. The Titan attacking another Titan at the start of Chapter 9 must be a hint at something, along with Ilse's side story. The "very light" idea is probably to defend the physics of having Giants. They definitely weigh more than a humans seeing how they have load footsteps and still fall with speed.