Our practice is to answer "Amen" five times to the Hasi Kaddish: after "Shemeh Rabba," after "Ve'yasmah Purkaneh Vi'ykareb Meshiheh," after "U'bi'zman Karib Ve'imru Amen," after "De'Kudsha Berich Hu," and after "Da'amiran Be'alma Ve'imru Amen." These responses follow the teaching of the Arizal, and of Maran (author of the Shulhan Aruch) in Maggid Mesharim – the record of the lessons he was taught by the angel who came to learn Torah with him. When we answer "Amen," we are expressing our wish that the words in the Kaddish should be fulfilled, namely, that Hashem's Name should be glorified throughout the world.
Interestingly, the Shulhan Aruch makes no mention of the first two "Amen" responses, after "Shemeh Rabba" and "Vi'ykareb Meshiheh." The Rambam mentions the first, but not the second. Both the Rambam and the Shulhan Aruch state that "Amen" should be recited after the word "Yitbarach." Regardless, the widespread practice follows the Arizal's teaching, to say "Amen" at the five points listed earlier.
The custom among many Ashkenazic communities is to omit entirely from Kaddish the phrase "Ve'yasmah Purkaneh Vi'ykareb Meshiheh."
Hacham Bension Abba Shaul (Jerusalem, 1924-1998) writes that if a Sepharadi is reciting Kaddish in an Ashkenazic congregation, he should recite the Sephardic version of Kaddish, unless this might create discord and make people upset. If he is concerned that the people might be displeased by his recitation of the Sephardic text of Kaddish, then in the interest of maintaining peace he should recite the Ashkenazic version of Kaddish. If he recites Kaddish together with Ashkenazic members of the congregation, then he should recite the Ashkenazic version of Kaddish, as he would otherwise cause confusion, given that the congregation is not accustomed to hearing "Ve'yasmah Purkaneh Vi'ykareb Meshiheh." If, however, it can be assumed that the congregation is familiar with the Sephardic text of Kaddish, then the Sepharadi should recite the Sephardic text. This is, indeed, the prevalent practice today in Israel, where most communities are familiar with both versions of Kaddish.