Dear Rabbi I was wondering if it is permitted to answer to kaddish if one is in the middle of prayer. For example, at mincha if one is still saying ashrei and the shliach tzibur start to say kaddish, should one answer? Or at sharchrit if one is saying alenu or the shiur shel yom and the shliach tzibur has started to recite kaddish whilst you are in the middle of the prayer?

Shalom, Thank you for your question. The laws of when you can interrupt your own praying to answer kaddish depend on what prayer you are saying at the time. There are places in the service when you may interrupt and answer Kaddish, and other places where you must just pause and listen to the answering of Kaddish, without joining in yourself. You can find these laws explained in a clear manner in English in the back of the Artscroll siddur. In short – to answer your examples, in both cases you should answer Kaddish, then continue with your own prayers. Blessings.