The original video for Bad Apple!! is one of the most well-known Touhou videos. Here's the original, together with English subtitles:
http://www.youtube.com/watch?v=VzEUeWnV73U
Why is the song called Bad Apple? There is an apple in the video but I don't imagine that's why. It matches the lyrics decently, but it still seems like a strange name for a song.
Also, all of the characters in the video are black and white silhouettes. Which characters are represented and in what order?
The song "Bad Apple" was originally the stage 3 theme from Touhou 5 Lotus Land Story. The popular version by Alstroemeria Records is a lyrical remix of that. Because Elly was the boss for stage 3, she makes an appearance towards the end of the video despite being a minor character.
There isn't any real explanation in the game as to why the song would be called "Bad Apple". Many original Touhou music pieces have names that don't really match the plot in any way, and as far as I know ZUN has never specifically explained this title. However, it is true that the popularity of the remix may be in part because it casts the series in a somewhat darker and more serious tone than the ordinary moe artwork, as the name would suggest.
As for the characters, I'll list them in order of appearance. The times correspond to when they first appear, and the names link to the relevant articles on Touhou Wiki.
0:28 Patchouli Knowledge (パチュリー・ノーレッジ)
0:36 Remilia Scarlet (レミリア・スカーレット)
0:50 Flandre Scarlet (フランドール・スカーレット)
1:03 Saigyouji Yuyuko (西行寺 幽々子)
1:18 Shiki Eiki Yamazanadu (四季映姫・ヤマザナドゥ)
1:25 Fujiwara no Mokou (藤原 妹紅)
1:32 Kamishirasawa Keine (上白沢 慧音)
1:45 Houraisan Kaguya (蓬莱山 輝夜)
1:51 Prismriver Sisters (プリズムリバー三姉妹), from left to right, Lyrica, Merlin, and Lunasa
1:59 Chen (橙)
2:00 Yakumo Ran (八雲 藍)
2:01 Inaba Tewi (因幡 てゐ)
2:02 Reisen Udongein Inaba (鈴仙・優曇華院・イナバ)
2:11 Kagiyama Hina (鍵山 雛)
2:22 Yakumo Yukari (八雲 紫)
2:27 Hinanawi Tenshi (比那名居 天子)
2:41 Ibuki Suika (伊吹 萃香)
2:48 Alice Margatroid (アリス・マーガトロイド)
2:54 Kawashiro Nitori (河城 にとり)
3:02 Kazami Yuuka (風見 幽香)
3:09 Elly (エリー)
3:20 Hakurei Reimu, PC-98 appearance
3:24 Kirisame Marisa, PC-98 appearance
As Alana has already suggested, the generally accepted theory is that the title comes from the saying "One bad apple spoils the barrel" [1], [2], but I do not know whether this has been "officially" confirmed by ZUN himslef. AFAIK the only thing ZUN has explicitly stated about this song is that it is like his older composing styles, but since it fits the stage, it should be okay. But then again, ZUN never reveals everything about his works.
It's also worth noting that this video is based on a very-quickly-made sketch (MS Paint stuff) by someone else. The original "author" uploaded the "storyboard" saying "I want to see a video like this. Somebody draw it please?" This storyboard remained mostly unnoticed until more than a year later, when somebody with an ability on the level of drawing cool silhouettes came and uploaded the famous video.
The original "author" never said that the video should be in black & white, but it works very well. Although the choices, the order, and the timing of the characters' appearances in that video follows the storyboard almost exactly, the comparison (http://www.youtube.com/watch?v=RkHFbIIQ9Tg) can be quite amusing.
Two of your questions have already been answered correctly (1 and 3). To answer question 2, I believe the song is called 'Bad Apple!!' because of how the lyrics correspond to the old saying "One bad apple", which refers to a rotten person, someone who is all around bad, etc. and the lyrics describe someone who is a "Bad Apple", or someone bad to the point of being worthless, and the singer in the song wishes to change, and have her hateful heart go from "Black" to White".
My theory about the meaning is that the song is telling us that we have to make a choice in our life. A very heavy and deep choice. The choice gives us two options. We can have a clean and pure heart, or a very dark heart. The song tells us either choice we make that we will both lose and gain something. It tells us to think hard, and don't choose right away. Either way we choose we will still feel agony and joy. I don't know for sure if it's the real meaning. It's just the message I feel from the song. I honestly don't care what the real meaning to the song is because they both are pretty good meanings. Either way I will still listen to the song because it's a great song. Tell me what you think it is. I really would like to read your thoughts you guys!
Ok so i may be wrong and this might be already writen down so please bear that in mind.
Im acually listening to lyrics and i believe its saying how the person "aka" the singer is saying how she's nothing she's nor good or bad she is in between and she is saying that its pain full
"It will never change",this is one of the lyrics saying that no matter what she does she will stay the same
In the english lyrics she asks"who are you idk what this is but i think that the "you" is the bad apple
I also have another theory the theory is that she is a vocaloid and the creator aka the one that is controling she is telling her to do certen tasks and she is being abused i think but pls dont hate?
Anyway i thing that the person singing the song is in the middle the ying yang represents "other people" and the other people in video is her and it changes constantly that meaning she is not black or white
"You can tell me what to say you can tell me where to but i dout that i would care and my heart would never know",is on of the lyrics but like i said before who is "you" thats up to you
