You have two different questions there.
First: should "I" or "me" be used, and second after "who" should the verb "to be" be conjugated in third person, due to the relative pronoun "who" or should it be conjugated according to the person preceding the relative pronoun?
The answer to the first question will depend.
There are two relative pronouns in English to identify a person "who" (which is nominative) and "whom" (which is accusative). Sadly in the last years, especially in the united states the use of "whom" has lost popularity. So the question "whom are you speaking to?" is more likely to be "who are you talking to?" in the united states version. So "who" tends to refer to the nominative and the accusative in modern English in the united states (Not in the UK or Australia where the use of "whom" is common).
Going back to the first question. the sentences:
It is I who... (relative pronoun agrees with nominative form of "I·)
E.g. Is it I who did not say a word.
It is me whom... (relative pronoun agrees with accusative form of "I")
E.g. It is me whom he offended.
But since in the united states "whom" is not used very often you may have to use "it is me who". And you may end up with "It is I who did not sat a word" and "it is me who he offended".
You can find more examples in this website:
http://learnenglish.britishcouncil.org/en/english-grammar/pronouns/relative-pronouns
As for the second question. Should the verb "to be" agree with the relative pronoun or with the person preceding the relative pronoun.
In the sites recommended by CJ Hepp it says that they may agree with the person or with the relative pronoun, I would go with the relative pronoun.
So, I personally (can't say that otherwise is wrong) would highly prefer:
It is I who is waiting here,
Rather than:
It is I who am waiting here.
Which sounds weird (not to say wrong) to me.