Behodar:
I'd have gone with "I" for both of those; as DarthKermit pointed out, if you make it "I am" then "I" is clearly correct. For the rephrased sentence, "I have" also seems correct to me, so again I'd go with "I".
If you add "am" to the end of the sentence, that makes it correct but it does not mean that it is correct to use I without am.

