please help, what are the sources of saying Brichu and Omein . who says what minhag

Thank you for your question, I'll quote the peninei halacha (Hilchot Tefila 23;11) who explains it nicely: There are differing customs regarding the response of “Yehei Shemei rabba….” According to the Ashkenazic and Yemenite (Baladi) minhagim, we conclude, “L’alam ul’almei almaya.” According to the Chassidic and Yemenite (Shami) custom, we add “Yitbarach” as well. According to the Sephardic minhag, we recite until “d’amiran b’alma.” Another difference is that after “Berich Hu,” the Ashkenazim answer “Berich Hu” and according to the Sephardic minhag, whoever succeeds in finishing until “d’amiran b’alma” responds Amen, and whoever does not, refrains from responding to “Berich Hu.” See the comment there where it is explained at length. All the best!