A "gimme" means the last shot was as good as in, or the next one?

Dooley is correct about the score - you'd give yourself a 4. However, what he says about giving putts in competition is only partially correct. In medal play (like the way the pros play most tournaments - every shot is counted) there are no gimmes. But in match play (the score for each hole determines who wins that hole) an opponent may give a putt to a competitor. Even in friendly, casual play you should always wait for a "gimme" to be given by someone in your group vs. assuming it's good and just picking up the ball.

It means you do not need to make the putt but you do need to count the stroke. So in your example the correct score would be 4.

In non-competitive rounds it is customary for players to give putts that are "inside the leather" meaning the putt is no further away than the length of the putter grip.

This practice speeds up play and is done as a courtesy to your playing partner.

"Gimmes" are not allowed in competitive rounds.

The 'gimme " refers to the next shot to be played. It is a concession by the opponent. In official tournaments which are based on gross scores ( total strokes) gimmies are not allowed. All holes must be finished by the competitors. One who doesn't " hole out " would be disqualified from the competition.