Re: the outline question in the original post.
The skin tones have a high lightness and a low chroma (saturation). The skin outline has a med-low lightness and a med-high chroma. If the background also has a med-low lightness and a med-high chroma then the outline will disappear (or seem very weak). If the background has a low lightness and a high chroma then it creates a ramp from background to outline to skin in both the lightness and chroma components. The character becomes connected to the background rather than separate.
Possible solutions:
Keep the character on a background with low saturation and medium or higher lightness. This preserves the contrast with the outline.
Switch to a black outline around the figure (but not internal to the figure).
Change the outline based on the background colors. This can probably be done on a level by level basis, depending on how the game is set up.
On the figure:
The hair is cute. It reminds me of the style of Ben Caldwell (a cartoonist / comic artist).
The figure has a square face and broad shoulders making the character seem androgynous. The position of the green stripes, both shifting the left, makes it look like the character is hunching over.
A sequence of edits:

1) Original
2) Moved the chest over to straighten the hunch
3) Tweaked the hair, and face. Crushed the shoulders and now the mass is carried around the hips. I didn't know at the time what sort of game this was for, I think this would match the jump and run style on the web page you linked. The edits after this would be tough to animate.
Changed the outline to a dark blue, to make sure it contrasted with the background.
4) Added mass to the legs to pull the center of gravity down more
5) Finished the legs (chicken legs!). The shorts are angled to match the legs, but need to be a pixel or two longer down the thighs.
6) Converted to skirt/dress. Needs some color.
Thanks for posting, this was fun to edit. Good luck with the game!
Edit: I decided I didn't like the chicken legs and the skirt was too short, so one more:

Which is probably useless for a run and jump game, but I could not let it go.

Tourist