How can I soften the closing/slamming of this gate?
The holes in the top of the spring are used to increase or lessen tension on the spring. It's the same principle you will find on a spring-loaded barrel hinge. You should find a pin in the last hole on the barrel that is up against a stop. Place a narrow metal rod like a small screwdriver or allen wrench into one of the holes and rotate the top of the  barrel to lessen tension on the pin and remove it. You can then reinsert the pin in a different hole to give it the proper tension.