Can someone explain to me what the difference between environment and local parameters is?
Question 2:
In a vp, there are vertex attributes besides the basic ones (like primary color, sec color, fog color, ).
What happens to these in the fp stage? They are no longer accessible?
Environment parameters apply to all programs with the same target (e.g. GL_VERTEX_PROGRAM_ARB or GL_FRAGMENT_PROGRAM_ARB). Local parameters only apply to the currently bound program.
What happens between the vp and fp stages is that any parameters you write out in a vertex program get interpolated across the triangles and can be accessed from the fragment program, now on a per-pixel basis. You are limited in which vertex attributes can be written out of the vp and read into the fp. See specs for further details 
– Zeno