This correspondent is identified in the published Igros Kodesh only as "Yitzchak Meir HaKohen" (about 5720–5730, 1960–1970). The letters appear to be to one person, apparently a writer or publicist, but I could not identify him from published sources.
Unity amid disputes. Even amid communal disputes, our mission is to fulfill our task (IK 7054), and true unity comes through Ahavas Yisrael rooted in uncompromising adherence to Torah (IK 8864).
Purim campaigns. Every child should personally fulfill the mitzvos of Purim (IK 7598), and communal efforts can inspire many Jews, even distant ones, to do mitzvos (IK 7608).
Public communication. The Rebbe thanked him for publications he sent (IK 9455), stressed clarity and responsibility in public communication (IK 10165), and explained that public denials are sometimes necessary, not for personal honor but to prevent harm to the truth (IK 10194).
Sources: the Rebbe's letters cited above.