a 'slur' also means that that part should be played as a whole, doesnt mean that without a 'slur' you should play it with pauses. So that third notation, just play it as it says.
I cann't see the images, your gays can see it?
"Played as a whole" as in; the notes should be mixed together, creating a "slurred" sound. If you play the notes in image 1 legato, without pedal, you should get the right effect. Try this: Hold the first note down and play the second note, without releasing the first. When you reach the third note, lift your fingers from the first two notes, and the play the third note through the fourth note. All of this without pedal.Of course later you will encounter much longer slurs, which require the use of the pedal. For example, below, in this bar from a Mozart sonata, the slur is written across every note in the bass clef; so it becomes easier to apply some pedal, rather than connecting each note as I explained above.The notes in image 3 are just quavers. They are meant to be played as two separate notes. Not staccato, and without slurring them.
The slur is not to be confused with two other similar musical symbols. The tie is a curved line that links two notes of the same pitch to show that their durations are to be added together. The ligature or phrase mark is a curved line that extends over a passage which is visually indistinguishable from the slur, and indicates that the passage is to be interpreted as a single phrase.