Well, what can I say? I don't see where your process is FLAWED per se, but I do see room for improvement. I don't see how you should 'learn' the fundamentals since you already know them somewhat, but you're not UTILIZING them to their fullest. Any talk about your workflow without having proof of you you work has been moot up until now, it seems.
I see you have a good workflow that would allow you to incorporate more design choices while animating - so why not try to help you do it a bit better?
I'd also like to say that I enjoy some of the stiffness of the animations, since not moving things too much will preserve symbolic value (on the most rudimentary level) in sillhouettes while things are moving around on screen. This does have good points, I don't see why it's suddenly such a sin to animate like that. With that said I still think some movement here and there should be in order. Moving pixels around is good stuff.
There is something that differs between pixel art and traditional animation and that's how easy it is to move things around and repixel, clean up, fix things, etc. Having a static torso when the limbs still move doesn't have to be horrible, you can just erase it, make the shoulders and hips work and then repixel it. Seriously. You can. And no, it doesn't mess up your workflow horribly. And yeah, if the legs and arms are awfully animated you've gotta redo stuff. Luckily robotacon doesn't seem to have messed up horribly here since the animations generally work except for some movement details we expect to see that aren't there. Or am I missing something? Are these sprites awful beyond repair? I don't see it.
Anyways, enough whiteknighting, Robotacon, since your rendering tech doesn't allow for subpixelling in a good way and you want things to still move smoothly, know this: Exaggeration is good (hi, I'm obvious) and it's better than you seem to think it is since your animations don't have a load of it. Old man for example, hsn2555 did that radical thing with the up-down bob and if you see it like I do, it added smoothness to the animation even though it made it move lots more. At the same time when things move at least one pixel per frame, that creates smoothness, as opposed to the clicking stuttery motion that appears when things stand still for several frames, that catches the eye MORE than if things move more vigorously.
So the critique I have? Elaborate on hsn2555's edit's ideas. Add weight in a logical sense, make him weigh DOWN on that cane, with this body, with his back. Add more shoulder movement. Maybe add some wobble to the cane-arm? There are things you can do within these frames that will squeeze more ANIMATION out of this old man. Take a stick and use it as a cane, walk around. Feel around and look for characteristic movements, find circular motion, pendulum motion, introduce it to the character. Try to move things more that you'd usually do - since you can't use subpixel animation, just MOVE things. Move them more than they should move logically - that's my suggestion.
Grah, this is just a miserable little pile of opinions, but I hope it's more than just empty talk.
Also, robotacon, drop the defensiveness. I do see your point, but when you manage to come off as defensive, the people giving you critique will just restate their original points ad infinitum until you 'get them' instead of elaborating. And this thread is already heartbreaking (for a sissy fellow like me). So try to bear with it. And good luck!
EDIT: I saw your new version now. Err. Quick points: Legs feel very snappy when they leave ground, like they POP off the ground. any way to fix that? Also his head LOOKS like it moves on its own, so I believe you should work more on extending that movement to the whole spine. That's all for now!