I would like to know the chemical components of "Silly String" and
their concentrations. I would also like a brief explanation of the
chemical mechanism involved in each step of the reaction, including
the initial states of all chemicals, the propelling reaction, "string"
formation and solidification.

The composition of silly string is a highly guarded secret. Its a bit
like asking cocoa cola to give you the recipe. Words like fat and
chance come to mind.
However, there are a few things that we can deduce. There are some
hazard datasheets available on the net for the product. These state
the potentially hazardous components as CFC's i.e. the propellant that
is used in the product. We also know that it was invented back in 69
and that it is a polymer based product. So it is probably a polymer
that dissolves to a degree in CFC type solvents. When it is propelled
from the canister the CFC evapourates (adding to global warming) and
the polymer dries out to leave the string. my best guess is that it is
probably a polystyrene or methacrylate based polymer.