To answer question 1, a large difference between phone and compact cameras is the lens. Phones typically have simple lenses with few elements which are designed to fit flush with the phone's body. Compact cameras more often than not have lenses which extend from the body when the camera is turned on, allowing them to be complex (having multiple elements to correct for various kinds of optical distortion), faster (i.e. they can allow more light in for shooting in darker conditions), and which can be zoomed optically rather than digitally.

Lens quality rather than sensor resolution is a major factor in the perceived sharpness of an image. The tiny, simple lenses in most phone cameras will tend to have a poorer optical resolution than the sensor they are recording to, meaning that beyond a certain point (5MP is plenty of sensor resolution for most web and print purposes) the sensor size becomes largely irrelevant.

This leads on to question 2. Can phone cameras match up to compacts in the future? Sure they could, but they'd need to come with better lenses, and that would mean they would look more like cameras with built in phones rather than phones with built in cameras.