**The first scenario you listed is correct.**

You choose a target and make an attack roll. If it hits, you roll for damage.
Then you may choose another target (the same target or a different one) and make another attack roll. If it hits, you roll for damage.
Additionally, you do not have to do two attacks when using the Attack action, you can choose to do only one if you so wish.

The 'Extra Attack' Feature simply allows you to do two attacks (or more as a Fighter levels up) whenever you spend your action on a turn to attack. This means that you make two completely separate attacks, not a single attack that you can roll again on if you miss (thus the third scenario is incorrect). Additionally, the second attack is not influenced by the result of the first attack, and regardless of whether you hit or miss the first attack, you can do the second attack (thus the second scenario is also incorrect).