Are the usages of "premise" correct .What words can I use here ?
1) A premise like commitment can help an individual to grow.
2) Integrity is one of the most important premises that a man can have.
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Neither of OP's examples are valid uses of "premise", for which OED defines only the "Logic" sense as applicable to the word in the singular form...
Clearly, OP's commitment and integrity are not "propositions". Integrity is easily described as a [character] attribute, but I wouldn't say that applies to commitment - for which the best I can come up with is life choice (plain action seems a bit weak in OP's context).
Note that there are a whole raft of different meanings for plural "premises", but those seem to be outside the scope of the question.