1 - Can projected geometry lines be modified on the projected plane or do projected lines remain just that "projected" to be used for reference and intersecting points to construct new geometry on the current work plane?
Projected lines can be modified if you remove the "Projected" sketch constraint from the projected entity:

This image shows the projected entity (the edge of the extrusion) - then deleting the projected geometry sketch constraint, and then the line behaves just like any other sketch geometry. There's nothing special about projected geometry - it's just regular sketch geometry, but it comes from another source object.
Be careful with cross-part projected geometry in an Assembly because that can (depending on an Application Options setting) create "adaptive" geometry. Adaptive geometry is very powerful - and very dangerous when used unwittingly!
2 - Can projected lines be separated from the projected plane and used as construction lines on the current work plane through a property setting or something of the sort?
Projected geometry (and regular sketch geometry) can't be separated from the current plane individually. You can redefine an entire sketch to a new plane, but I'm not sure that is your question. Might need more explanation to understand what you're trying to achieve.
3 - Once projected lines have been created and used can they be deleted or will the object lines that originally use them become "underconstrained"?
Projected geometry can be deleted, but just like a regular sketch, if you delete something you've used for a dimension, the dimension gets deleted with the geometry. You may have seen a scenario where the source object got deleted (or moved): That will leave behind pink projected geometry - indicating that the projection process is broken. Remove the Projected Geometry sketch constraint to fix it. (Note that in the example below you'd remove the sketch constraint from the line and the two endpoints.)

This shows the same example as previously, but I went back to the original extrusion and effectively "deleted" the edge which I had projected.
4 - Other than using an axis to snap parts together in an assembly when would an axis be created inside a sketch? I am not understanding the relevance of an axis inside a sketch when you can create any form of the work plane and project geometry as required to create new reference points.
There isn't an axis creation tool in the Sketch environment - it is a 3d model feature. You can project an axis into a sketch the create either a line or a point - but you're right, there's no point in having an axis in a sketch.
Hope that helps.
Peter