Given a forward reaction with positive enthalpy, is its reverse reaction be endothermic or exothermic?
Yes, in a reverse reaction the sign changes. That is because Enthalpy is a state function, one that depends on only the current state of the function. That means the energy required to push a reaction to its products would be directly reversed to push it back to its reactants. 

A key use of this knowledge is in Hess's law, and Born Haber Cycle.