Karatube is run by the team behind Karadeo. Questions, bug reports and removal requests all go through the Karadeo support form:
There is no sign in, so a playlist belongs to the browser it was made in. Open the same browser on the same device to see it again.
Some uploaders disallow embedding. Remove the song from the queue and pick another upload of it.
The queue's owner is the browser that created it. If you cleared cookies or changed device, start a new queue.