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Neither must be followed by nor and not by or. Either is followed by or: She drinks either orange juice or apple juice.
The first sentence is wrong because it makes all people lazy.
Similarly, Everybody doesn't like dancing should be Not everybody likes dancing.
As is a conjunction, and is usually followed by a noun or pronoun in the nominative case. Like isn't a conjunction, but an adjective which behaves like a preposition being followed by a noun or pronoun in the objective case.
To hire something is to pay to use it, usually for a short time, with one single payment: a suit, a bicycle, a rowing boat etc. To hire out is to offer something for someone else to hire.