I wish I had this music application

I've been struggling to learn to play the keyboards. It'd be nice to have an application that could help me.

Ideally, the application would allow a user to select from a set of preloaded songs, or to point her device's camera at sheet notes for a song that she'd like to learn. She would then be able to view the digitized version of the sheet notes and select and play segments of the song through the device's audio synthesizer. 

The application should also be able to "listen" to her play the song on keyboards, via the device's microphone, and offer feedback.  The parts of learning a song that I struggle with are: where to place my fingers, when to strike the keys, and how long to hold each note (basically, everything!)

The application would provide a visual guide of the keyboard and how to place the fingers to play a certain note.  It would wait for the user to play each note correctly before moving onto the next note, in this mode.

Another mode would help with pacing. The application could provide a visual representation of the ideal tone - with a rising edge, pulse, and falling edge - along with a visual representation of the tone that the user actually produced.  This visual information would hopefully allow the user to correct the timing - when to strike the key and when to release it.  Ideally, if this is done for a set of notes, the user would hopefully get a better sense of beat.

I've heard that many neural pathways are formed when a person learns a musical instrument.  I wish I knew something about how the human mind and how it changes when a person learns musical instruments.  I am not sure if such an application would be helpful in forming the correct pathways, or in long-term learning.