#2
Your fingers are fast enough, speed is NOT your issue.

The problem is that your fingers are not accurate or controlled enough, also it's likely that you don't know what you're attempting to play well enough or haven't practiced it enough.

So do what everybody does for every aspect of getting better on the guitar.

Slow down.
Concentrate on playing things accurately and cleanly.
Keep your motions as economical and controlled as possible - you can't "make" your fingers faster, you CAN make sure they're not moving too far and are landing exactly where they should.
Use a metronome to keep time, don't go chasing it - play at a speed your comfortable with until you're playing consistently without mistakes.
Actually called Mark!

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#3
Guy above pretty much said it.
Play slow at first, so you figure how to mute the other strings so it doesn't sound sloppy. Make sure both hands are working good together and don't just practice chormatic patterns that you'll NEVER use except when you're practicing at home. Instead, spend time one figuring how to play patterns in common scales and don't forget to use your pinky!