The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Vayehi (Shana Rishona), writes that if one is standing when the recitation of Kaddish begins, he must remain standing until he completes his "Yeheh Shemeh Rabba" response, reaching "Da’amiran Be’alma." Once he has finished his response, he may sit.
This Halacha is relevant to several occasions when Kaddish is recited, such as the Kaddish recitation after Hallel. As Hallel is recited standing, we are generally standing when the Hazan begins reciting Kaddish after Hallel, and we must therefore remain standing until we finish our response of "Yeheh Shemeh Rabba." It can also happen when an elderly person or Rabbi passes by, and one stands out of respect, and then Kaddish begins. In this instance, too, one must remain standing, as discussed.
It is customary to recite "Kaddish Yeheh Shelama" after reciting Tehillim, such as at an Arayat. After learning Torah She’ba’al Peh, such as Mishna, Gemara or Halacha, "Kaddish Al Yisrael" is recited.
It is forbidden to walk in front of somebody saying Kaddish, just as it is forbidden to walk in front of somebody reciting the Amida. However, if he has already passed the point of "Da’amiran Be’alma Ve’imru Amen," one may walk in front of him.
Kaddish yields great benefit for the soul of the deceased, which is why mourners recite Kaddish for their deceased father or mother during the year after the parent’s passing. However, since the wicked are punished in Gehinnom for twelve months, and we do not wish to give the impression that the deceased was wicked and thus requires Kaddish for all twelve months, it is customary in our community for mourners to stop saying Kaddish for one week at the beginning of the eleventh month. After this week, they resume reciting Kaddish until the end of the twelfth month.
The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes (in Siman 56) that if one hears "Nakdishach" and Kaddish at the same time, and he needs to choose to which to respond, he should respond to Kaddish. This often happens when one prays at the Kotel Ha’ma’arabi, and he hears several Minyanim in progress at the same time.
Summary: If one is standing when Kaddish begins, he must remain standing until he completes his response of "Yeheh Shemeh Rabba," reaching "Da’amiran Be’alma." It is forbidden to walk in front of somebody saying Kaddish, unless he has passed the point of "Da’amiran Be’alma Ve’imru Amen." If one hears "Nakdishach" and Kaddish at the same time (which happens very often when one prays at the Kotel Ha’ma’arabi, and several Minyanim take place simultaneously), he should answer to Kaddish.