It isn't for your own educational purposes if you're making it available for others to download -- that's called distribution.
Yes, exactly. As soon as you make it downloadable, it's not merely for your own education. You actively (but not maliciously) are providing a counterfeit mario game that, while great, isn't as polished as Nintendo's and so it is an inferior product (no offense - Nintendo spends millions on Mario), which hurts the reputation (even if just one person plays your game) of their brand.
You can keep the engine and gameplay style and still distribute your game, provided that you replace the art, music, and sound effects with original works. With your engine in seemingly good shape thus far, you could probably recruit an artist to work up some original artwork in a similar style pretty easily.
To clarify what Ravyne is saying, having an artist create "original artwork" for you does not mean, "original mario artwork", it means artwork that isn't Mario. It can play like Mario (gameplay isn't copyrightable), but it can't look like Mario or be called Mario. Same with the music - it can't sound like Mario. You can say, "I made my own Mario-like game" and use the name "Mario" to describe your game, but it can't be in the title of the game either.
Just basic copyright law. Nintendo may or may not call you out on it, but it is in violation of their copyrights, and United States law says that if they want to protect their rights from anyone (including Microsoft or Sony), they have to actively defend their copyrights against everyone (including hobbyists) even if it makes them look like bullies.
This isn't a matter of them taking your home or anything, just sending you a letter saying that if you don't take down the game they'll sue to defend their property. They aren't after your money, so not having alot of money isn't protection from their lawsuits, they are after defending their hard-work from being de-valued by others making less-polished versions that someone might think is the real thing.
Nintendo is so defensive of their intellectual property (and rightly so! It's their entire business!), that they've contacted this site in the past (www.gamedev.net) and have a blanket legal request to discourage Mario-related and Pokemon clones. I don't know if that's still in effect or not, though. You can make something like Mario, and you can say it's like Mario, but you can't call it Mario, or make it look or sound like Mario.
It's far better to just use your engine to make your own really cool product. Nintendo's really cool product is successful because they spent so much effort, money, and marketing on it, which is why they deserve exclusive use of it - it's their work. There is free artwork and music available online that you can use in your game... why take risks with the stolen Mario artwork?
The same applies to Mickey Mouse, Halo, Half-life, Pokemon, everything! If you create something new, the same applies to your own work - I can't make my game using your work (even if my game isn't charging money).
Your work looks very good though! Don't let it go to waste, but recycle it into something that is new, original, creative, and 100% yours to give away or sell.