Any of these phenomena would be visible to the naked eye if they occured in the Milky Way, or a neighbouring galaxy (such as the Magellanic clouds) and was not obscured by dust. At the distance of stars, all of these would appear star-like.
Supernovae have been seen, most recently in 1987, when there was a supernova in the Large Magellanic cloud. It had a peak magnitude of 2.9, (about as bright as gamma ursa minor, the star at the bottom of the Little bear constellation, furthest from the polestar). It was visible, but not spectacularly bright. Supernovae that have occurred in the Milky way have been very bright, outshining all the other stars. A supernova in 1006 may have been brighter than Venus. If it is close enough a supernova could be seen during the day.
All of these are highly energetic, and if you were close enough to see any detail (such as a nebula) with the naked eye, you would be toast. The exposive events (Supernovae, Kilonovae, Gamma ray bursts) would fade over time. Magnetars and Quasars are stable and would continue to shine. Remnant nebulae from Supernovae are visible in telescopes, the most well known is the Crab Nebula, M1.
A supernova in Andromeda would likely be naked eye visible, but not impressively bright, though it depends on the acutal power of the explosion, and other factors, like dust in Andromeda.
Supernovae are visible for months. Kilonovae fade faster. Gamma ray bursts may only last for a few seconds (though may be associated with a supernova that lasts longer). The visible element of a GRB might be visible, there was one that might have reached naked eye visibility, though there is no evidence that anyone actually saw it (it would only have been marginally visible in ideal conditions). Quasars are stable objects that don't fade over time, they are active supermassive black holes.
There are lots of other, more local things that can produce a "star" that brightens then fades: Planes have headlights, and as they turn the appear like a star that brightens then fades over a few seconds. If they are distant enough, the other lights might not be visible.