The Birkay Yosef (581:4) writes, that one must recite selichos and tachanunim, calmly, slowly, and with paying attention, and that it is forbidden to mention the Yud Gimmel Middos without kavonah (see also Kaf HaChaim 131:21), therefore, one who knows about himself that he is unable to have kavonah should refrain from reciting the Yud Gimmel Middos.
There is a well-known story with the Chofetz Chaim, that he once stopped his talmidim in the middle of selichos, and told them, selichos is not only about mentioning one's aveiros, Hashem already knows everyone's aveiros, selichos is about arousing oneself to do teshuva, therefore, during selichos one must accept upon himself to fix what he has being doing wrong until now.
Interrupting In the Middle of Learning to Recite Yud Gimmel Middos
R' Moshe has a Teshuva (Igros Moshe, Orach Chaim 3:89) where he discusses if one must interrupt learning in order to recite the Yud Gimmel Middos. He writes: Although the Rema (125:1) writes that if one has already said kedusha and he enters a shul and they are in the middle of kedusha he must join in with them as they are being mekadesh Shem Shomayim, and for this reason, if one hears a minyan saying Shema Yisroel he must join in, in regards to the Yud Gimmel Middos we don’t find such a thing. The Yud Gimmel Middos aren’t considered kabbolas oil malchus Shomayim and they are not on the same level as a dovar shebikdusha such as kedusha. They are said to invoke Hashem’s mercy on us, therefore, only those who are davening must say them. One who is learning and overhears a minyan who is saying them, doesn’t need to join in.
However, he concludes, the minhag is in fact to join in. R' Moshe speculates that the reason is, although there is no obligation, the more people that say it together the better it is, and it will invoke more mercy from the Ribbono Shel Olam. According to this minhag, one who is learning should interrupt his learning to join in, however, many people don’t.
R' Zilberstein writes: The above is only in regard to an individual learning, however, for talmud Torah d’rabbim, i.e. someone is giving a Daf HaYomi shiur, certainly, there is no need to interrupt.
