There are two basic scenarios that get a little confusing when players are going all in. Scenario 1 is when the player goes all in for less then a full bet, your case 1 and case 3 are covered in this scenario. Scenario 2 is when a player goes all in making a raise that is less then the full raise this is your case 2.
The big problem is that the answer to these questions have a lot of variables involved. The way it would be done at a tournament often differs then the way it would be done in a cash game, but not always depending on where you are playing. The only right answer to this question is what you agree on at the time.
The important thing is that however it is commonly done is not particularly important, this is really a zero sum thing when the rulings are consistent for everyone. What is important at a card game is that whatever way it is done is known to the staff and players and always done the same way. There is really no particular best way to define this, just kind of depends what everybody is most comfortable with.
One should be aware that the short answer to the question of “what is the minimum raise allowed after the flop in the following questions” is that it depends completely on where you are playing, what shift you are playing on, who is dealing, and who is on the floor. You should expect different rulings from different dealers and floor people. You will find no consistency with rules here. Even people who read the rules have a bad time understanding the rules.
When you come across this type of situation you should just ask, and then when it comes up again ask again, good chance you will get a different answer.