My friend keeps on responding to questions by just saying "I´ll". This doesn´t seem grammatically correct to me. However I would like to know what would be the proper use of that contraction.
I've never heard anyone as a native speaker say this or write this. Consider a teacher asking a question: "Who will answer this question?" A student yells out, "I will!" Another one replies, "I'll answer it, Mr. Jones!"
The contraction of "I will" to "I'll" makes the rest of the sentence shorter. If the entire sentence is "I will," the contraction is unnecessary. That is why nobody (except perhaps to be funny) says, "I'll" as a full sentence.