1) Mathematically related. See : http://en.wikipedia.org/wiki/Rate_law
2) Even though the reactant might be
unimolecular, bear in mind the polymolecular products
exist in equilibrium with the reactant.
3) k is related to the orders with respect to each
reactant, which is in turn related to the stoichiometry of the
elementary rate determining reaction. Conceptually, whether the
position of equilibrium (indicated by Kc) lies more towards
the left or right, and by how much, depends on whether the forward
reaction or backward reaction is faster (ie. kf versus kb), and by
how much. Hence, Kc = kf/kb.