I can handle the simplest examples
1) if rate equation is k[X] and there are other reactant, Y and Z say, then I can interpret that as [X] splits up (free radical or ionic) . The product is then very reactive and binds quickly th other reactants
2) If rate equation is k[A][B ] then I would suggest the reaction is rate determined by the collision of a molecule of A with a molecule of B to form an "activated" complex that then splits to form products.
3) Any higher order rate equation seems tricky, at least (see my first posting) to interpret.
Clive