laugh (verb): to express mirth, pleasure, derision, or nervousness with an audible, vocal expulsion of air from the lungs
hysteria (noun): an uncontrollable outburst of emotion or fear, often characterized by irrationality, laughter, weeping
hysterical (adjective): of, relating to, or characterized by hysteria
All are mostly grammatically correct but all differ significantly in meaning. I take it that the original sentence is attempting to express the juxtaposition and contrast of laughter and the extreme expression of hysteria. In which case:
- Brain was given to man to laugh, not to get hysterical.
The indefinite article indicates that a noun refers to a general idea rather than a particular thing.
"Brain was given to man" doesn't read right, "brain" should be used with an article and referred to as "a brain".
Also, the subject is missing, a human doesn't get "given" a brain like one would be given a birthday present, it reads better like "God gave man a brain" or "man biologically evolved a brain". In this context the correct structure would be something like "A brain was bestowed upon man" or "Man was granted a brain". You could say "man was given a brain (by a god or creation origin concept)".
Then with the second part, hysterical is an adjective that describes man, hysteria is a noun. The tricky part is that the comparison needs to be made between a verb and an adjective so I think "to laugh" and "to get hysterical" is fine and works.
- Brain was given to man to laugh, instead to get hysterical.
Should be "instead of" and then the adjective becomes "instead of getting hysterical" or "instead of becoming hysterical" or even "instead of reaching hysteria". This suggests mutual exclusivity, that is, man can either laugh or "instead" get hysterical. Laughter may lead to hysteria and hysteria may involve laughter so I don't think it is right to imply that man can do one OR the other.
- Brain was given to man not to get hysterical, but to laugh.
"A brain" was not solely given to man to laugh, this is how the sentence reads.
- Brain wasn't given to man to get hysterical, but to laugh.
"Was not given" and "not to get" has the same meaning, sentences 3 and 4 convey the same meaning.
If I was writing this in English from scratch I would use something like:
- Man was given a brain to laugh, not to become hysterical
- Man was granted sentience for the purpose of laughter, not hysteria
- Man was not given a brain to become hysterical, but merely to laugh
- Man was granted consciousness to laugh and not to be plagued with hysteria
- A brain was not bestowed upon man for hysteria, but for laughter
- A brain was given to man for laughter, not hysteria
- A brain was given to man for laughter, not to become hysterical
- A brain was given to man to laugh, not to become hysterical
- A brain was not given to man to become hysterical, but simply to laugh
- Man has a brain so that excitement can be controlled