1) The benefit you forego by not selecting the next best opportunity.
2)The rate used to account for the time value of money. The higher the risk, the higher the discount rate you'd use.
3)Several different ways. Typically a risk-free rate plus a risk premium. Risk premium determined a number of different ways, WACC, etc.
4) Linked? No. Correlated? Sure because the risk-free rate is generally something like the 10-year bond or LIBOR.