Are the angels infallible, and are they punished if they err, and do the angels on the right and left remain with a person throughout their life?

Angels are infallible and were created for obedience. They are: "those who do not disobey Allah in what He commands them and do what they are commanded," and "they act by His command," and "they do not disdain to worship Him, nor do they tire." They are messengers of Allah, and messengers are infallible.