Is it a condition when making up missed Ramadan fasts that the duration of the make-up fast be identical to the duration of the day that was missed? And will a Muslim be rewarded for the extra days he fasted as a precaution, even if they were not obligatory upon him?

It is not a condition that the days of making up (fasts) must be equal in time to the days of performance, due to the Almighty's saying: "then a number of other days." And whoever does not know the number of days they owe to make up, they must investigate and strive to determine them. Being cautious is better to clear one's conscience, and if one overestimates, they will be rewarded with the reward of a supererogatory act.