Questions about choosing between the prepositions "to" and "for".

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“Indispensible for” vs, “indispensible to”

What is the difference between "indispensible to" and "indispensible for"? Likewise, between "it is important to me" and "it is important for me", which one is correct?
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“For nothing but (to)…”?

"You should do this, even if for nothing but to test." "You should do this, even if for nothing but testing." The first sentence feels acceptable, but is it wrong because of "for"? After all, it ...