Derivatives - Future Price Question

I have a few questions regarding Derivatives:

  1. “If futures prices and interest rates are uncorrelated, forwards and futures prices will be the same”, I believe that in this case, the futures price is at inception (which is also equal to the fixed agreed-upon price) because later the future price would fluctuate based on the underlying asset price and lower compounding period to converge the underlying future spot price. Is it correct?
  2. The value of a forward contract at expiration = S(T) - F(T). In this case, the F(T) is calculated based on the P(0) - the cost of capital which means that S(T) - F(T) also accounts for the cost of capital at expiration.
    The value of a forward contract before expiration (at t<T) = S(t) - F(T)/(risk-free rate)^(T-t) - (cost of capital)*(risk-free rate)^t which means that cost of capital is eliminated in this calculation.
    I want to ask that why the cost of capital is accounted at expiration but not before expiration?
  3. About Forward Rate Agreement, we use FRA to hedge interest rate risk for future borrowings/lending rights? So there is only a transfer of difference in the contract rate and Libor based on the notional principal. And how synthetic FRA works to replicate real FRA?

Thank you so much!!!