Adding "ever" to a sentence is quite common in german, but very informal and colloquial.
It is mostly used to emphasize an opinion and probably developed, as it has already been stated, from using "aller Zeiten" as emphasis. A sentence in which "ever" occurs is significantly shorter, since in most cases it lacks a verb and any pronouns.
For "Es war das schlimmste Unwetter aller Zeiten."
you can also write: "Schlimmstes Unwetter ever!"
Both sentences have the same meaning:
"It was the most devastating storm of all time."
It's always [superlative of adverb/adjective] + [noun] + "ever"
Other examples would be:
"Bester Kollege ever!"
(He/She is the best colleague there is)
"Schlimmster Kurs ever!"
(This is the worst lecture of all time)
"Bestes Bier ever!"
(This beer is the best one I've ever tasted)
You can also use "ever" as you would use "aller Zeiten" in any sentence, like:
"Es war das schlimmste Unwetter ever.", but this isn't as common.
Concerning the insult your assumption is correct: "Behindertster" is the superlative of the adjective "behindert", which means "disabled", but also "retarded", which in this case would be the right translation.
So she assumed her teacher was mentally disabled/dumb.
For insulting someone as disabled in a sense that he is incapable of normal physical activities someone would rather use "Krüppel", which means "cripple".
Both insults are quite severe and almost never used in a "friendly" way, unlike other insults which can be ways of teasing a friend (similar to "I hate you" in english).