One can classify reactions by their overall order of reaction. These can be found in the literature, journals, books, tables, etc., see the footnote on p.75. They can also be determined in the laboratory. It is a function of concentration of species participating in the reaction and whether or not there is a catalyst present. It is related to the strength of the chemical bonds that must be broken and formed for the chemical reaction to take place.
Many chemical reactions are elementary.
The only way to find the rate law is by experiment. See chapter 5. The equilibrium constant and it's relationship to the concentrations of reacting species is determined by the thermodynamics Not by kinetics. For irreversible reactions the rate law equation is simpler and so are the computations involved in reactor sizing. Temperature affects the equilibrium constant, K c and thus the rate law, through the Van't Hoff equation.