I am curious when you talk about shading inconsistency do you mean within a piece or between the different drawings? Or do you mean the lack of shading in backgrounds versus the foreground?
I just want to clarify that I'm no where near being a professional 2D artist, my opinions are solely based on my experiences in 3D and the various lighting tutorials I've looked at.
This is primary a critique, on your 2nd post image, I'll give some thoughts on your first post images also at the bottom. Something to keep in mind is that our eyes are drawn to bright colors. The white's in the image are what I would say distracting the viewer from what is the real focal point. A way around this is to like you said, de-saturate the scene a bit while maintaining the quality on the character. Or pronounce the shading on the character like you did with her hair. Another technique to consider is guiding the player to the intended focal point. For example, her socks are already colorful, you can take those, brighten them up a bit, and slowly divert the viewers eyes upwards by a secondary object at the waist up until the top. Now of course this will all happen instantaneously for the viewers, but the idea behind this is to subtly divert them to where you want them to look. When I first looked at the image it wasn't the character that first caught my eyes but the fridge. This is because the whites are the brightest.
If the whites needs to be in the scene because that object's intended color is white, what you could do then is cover up as much of that surface as possible. Taking the fridge for example, have small notes, or decals, have something on the countertop to the left of the fridge. Have some cereal boxes on top, put a few misc items inside the fridge. Doesn't have to be a lot just a few items to break up the color. Cheap way to create contrast without destroying your color scheme, and divert the attention to the correct element in the scene.
As far as shadow goes. The inconsistency I'm talking about are the shadow areas on the character, fridge at the bottom, soft shadows v.s hard shadows and the intensity of that light source. The overall brightness of the image makes it feel like a direct light from the sun. Well I mean not literally having a sun above her but you get what I mean. And it's hard to pinpoint the direction of the light because various shadows are in places that convey different light paths. Looking at the characters hair, her left side is in shadow, her back hair is lit but her shadow's silhouette is being projected to the right?. Her shadow on the wall indicates that another light source is coming from the left? and it doesn't look like it's the light from the fridge. The bottom section is also casting shadow to the right, and if the secondary light source I assume is coming from the inside of the fridge, because there's a secondary shadow of the character going off to the bottom right, then the bottom shadow makes sense, with the exception that it wouldn't stop there and continue up to the side of the right countertop. The right countertops shadow at the bottom seems off too, the length of that shadow of course taking our perspective into account, shouldn't extrude pass that left bottom most corner if the light is coming from the top and being lit by the fridge's light.
Lighting or in this case 2D shadowing, is tricky and I'm not the most qualify to make this assessment, as I'm also learning how 2D shading works. Don't take what I've said at face value but as reference and compare it with critique from other's and make your own judgement based on that.
Your 1st post pretty much falls in line with what I've already mention above about shading. If you commit to shading one part, it doesn't make sense at least to me not to shade the rest. It breaks the composition. On another note, I highly discourage you from creating darker outlines, this will definitely break the composition you have already setup. There are other ways to make your image "pop" without being destructive to the overall composition. Another example is to slightly shift the hue values down or up and to use the correct color scheme in your shading. What I suggest is, use 3 different color value, the mid, high and dark tones of your color pallette . If you apply this to your characters skin kind of like how you did with the hair, by slightly using the high tone to create highlights in the apporiate places this doesn't have to be a lot nor in a lot of places, but use it to guide the player, and using the dark tones to shadow and create contrast between the high and mid tones, you can easily and cheaper draw the attention to the correct area's without being destructive to the overall composition.