Style
Actually, pretty much all of these tips are universal to
digital art no matter what style you use. A lot of the examples are in anime/manga styles because those were just the examples I found first, or happened to have on hand.
Rushing
This isn't about what you like looking at. This is about winning art contests. "Rush and get it done" is good advice regarding contest entries because you have a deadline to meet.
It's better to have a finished piece that's a bit rushed than to never finish some giant masterpiece. For your own personal masterworks, take as long as you like. ^^
In general, learning to work more quickly will help you immensely in every regard.
If you look at the best artists we've got online, they actually work really quickly. This helps then churn out 5 amazing images in the time it would take you to finish one above-average one with the same level of detail. It's because they've learned to work quickly. How do you get to the point where you can knock out a great piece in a short amount of time? By practicing! Contests allow you practice stuff
and get prizes.
I think, though, that you might be a bit confused at the difference between rushing something ambitious (and getting a decent image as a result) and just doing a quickie piece. Rushing doesn't mean you skip details, it means you draw them quickly. Skipping details is something you do if you're just doing a quickie piece. I'll add a note about the difference to prevent others from the same confusion. ^^
Backgrounds
I didn't say backgrounds were
required, I said they are
advised. If someone running a contest doesn't want backgrounds or says they specifically want something, then go for it. But in general, backgrounds will improve your prize placement.
Case Study
Every main winner in this contest has a background. The highest-placing images without backgrounds are category runner-ups: Chibi Runner-up (but it's animated), Cutest Runner-up, Not Cute Runner-up. Images with backgrounds won all of the main prizes, and outplaced images without backgrounds in the categories.
Percentage of entries with backgrounds: 33%
Percentage of winning entries with backgrounds: 66%
Including a background gives an image a more finished quality, displays more effort, and shows more skill!
A picture with a background is more likely to win a prize than one without a background. If you have two artists of the exact same skill level and one draws a background and the other doesn't, the one that drew the background will win probably around 90% of the time.
The only time a picture without a background beats one with a background is when the artist in question is much more skilled. On many occasions artists of slightly lesser skill have beaten better artists because they draw a background.
Do you
have to draw a background? No! Of course not! Will you win better prizes if you do? YES, obviously!
Someone could easily beat your contest entry example by doing a dark piece that has a dark background to match. If their art skills aren't as good as yours, you might still beat them. But if they are as good, it's likely they'll beat you.
I'm not sure what you're saying people prefer. No backgrounds? I don't think the evidence bears this assertion out, at least as far as contest results are concerned. Dark art? Well, sometimes people specifically ask for that because they prefer it, but actually most people seem to prefer cute art. (I don't prefer cute myself, I'm just saying.) But then, I'm not making tips specific to doing any one style or theme, I'm trying to provide tips that can be used regardless of whether you're working on a cute piece or a dark one, or something else altogether! ^^
I'm also a little confused about the comments you say you get on your art. I'd actually say your coloring is rough-looking, more painted than smooth, and while your stuff is nice, I wouldn't say it's particularly detailed. Have you posted stuff in picture post? You might be able to get some better feedback so you can improve! Or maybe on dA or something where you can get better feedback on your work.