That's a lot of improvement! Runensucher is absolutely right about my edit being in a different style. Your initial doodle already had a lot of good stuff going for it, and the ways in which I adapted it aren't universal advice. I'll try to go over why I made the changes I did, and hopefully that'll help you.

When I talked about the proportions inhibiting cuteness, this is what I meant:



The face on the left has pseudo-realistic proportions. The face on the right has all the features moved down and the eyes slightly enlarged. This advice doesn't work universally, but generally we find proportions like these cuter. This is also true of head to body ratio; we find larger heads cuter, probably because we associate these proportions with babies.

If you look at the source material for reference, you can see that moogles were designed with these proportions in mind.



This design has a big bean-shaped head with low facial features and a small round body with cute little limbs. The sharpness of the ears and wings accentuates the roundness of the head and body.

Just by emulating the moogle design, your sprite already has a lot of these traits. This is a matter of personal taste, of course, and my modifications of your sprite were pretty extreme, but I find that I even prefer a version of your sprite with minor edits, like so:



I just moved the face down a couple pixels and used the shading colors to round out the body a little. EDIT: and messed up the wings in the process because I wasn't paying attention, oops 

Your colors are already looking much better, so I'm not sure any tips from me will help at this point, but I'm happy to share my process.

When it came to recoloring your sprite, I saw that all of your shading colors were very close to each other on the color map:



So first, I cut out all the super-similar colors:



Then, I reshaped:



I decided that the black and the purple were rarely used and pretty similar, so I combined them, darkening the purple and making it bluer so it could be easily distinguished from the red. I didn't know what kind of background you were eventually going to put this piece on, so I used my new dark color to add an unbroken outline, because dark outlines go well with most backgrounds:



I knew from experience that because the red was between the purple and the cream in both hue and brightness, it could be used to soften the transition between them. Some of the transitions were still too harsh, so I selected another color between the cream and the red (again, between them in both hue and brightness) and used it to shade/add detail, resulting in my final sprite:



That was a reenactment of my actual process, which involved more trial and error at each stage. I guess I figured out my colors by working with your colors! This particular ramp works because each color is darker and closer to purple than the previous color. By going yellow-orange-red-purple, we make a smooth transition.

Let me know if I can clarify any of this. I'm interested to see how you progress on this and other projects!

Your work so far looks good! For details on smaller sprites, especially when making eyes, anti-aliasing is super helpful. I used the gray from the cloak to smooth out the harsh borders of the skin.



I personally find it easier to make sprites from a slightly higher perspective, so I also moved some of the features down/reworked the hair. This is a different style than the one you're working with, but I hope it gives you some ideas!

This template may help you:

http://opengameart.org/content/seamless-tileset-template-ii

Because of the style of tileset you're making, this template has some superfluous tiles, but if you remove those, it should cover everything you need.

I googled as hard as I could, but there's a relevant tutorial which I failed to find. Does anyone know where to find that excellent guide about making efficient grass/dirt tilesets? It advises breaking a tileset into smaller chunks, as in, going from a 2x2 grid of 16x16 grass tiles to a 4x4 grid of 8x8 grass tiles. I think that the whole guide is a big image file on deviantart or something, which makes it tricky to google.

I'm not sure I'm correctly understanding your problem with Tiled. Did you modify an existing terrain? That could explain the weird water properties. You might have better luck using the tilesets tab instead of the terrains tab.

Edit:

I couldn't seem to replicate your problem. Is this what you were aiming for?

Nice animation! Because the chest is rocking back and then thumping forward, I think it makes more sense for the impact dust to happen when it lands. See if this is any better:



It's also a little weird that the chest top appears to be rounded when opening, but looks completely squared off once it's resting in the open position.