Does Katherine Have a Daylight Bracelet?

Vampires can be given a second or replacement daylight ring, as long as it's enchanted for them as it is shown that Katherine Pierce had two; an amulet during the 1800's and a bracelet during the present day.

Does Elena get another daylight ring?

Elena is the first vampire to have their daylight ring destroyed in either series by magic. Jo makes Elena a replacement daylight ring between this episode and Prayer For the Dying in order to practice her magic.

Does Klaus have to wear a daylight ring?

Without their rings in the public, they would expose themselves as vampires. Since they were the first of their kind, only the originals owned daylight rings, and for many decades, it kept up, until the spell to create the rings was slowly revealed, and more and more vampires started to wear Daylight Amulets.