Yes.Is it enough if I click on "quickpet" -> "xenialpup updates" ? How often should I do this?
For anything that is really needed to fix a bug or provide an improvement.
Maybe do it once a month.
That is about as close as it gets to feeding you updates and bug fixes in Puppy. That is something 666philb offers in his Puppy versions.
Internet browsers are about the only other thing you need to keep updated.
Those have their own builtin way to update.
You will have to set them to auto update or run their update whenever you want to.