In simple terms a roof box will adversely affect the fuel consumption as it is adding to the frontal area, the difference may not be that great, but you cannot argue with the laws of physics. An odd mile per gallon loss may not be apparent but over time will add up.
When towing though it may reduce the drag created by the front of the caravan and help but should be removed at other times.
Any thing heavy could affect the handling but it will vary according to the car and its suspension.
As for the weight, I am afraid you need to know all the weights of everything in the car to see if you are overloading it.