This summary is drawn from the Rebbe's letters to him (from the late 1940s to about 5722, 1962); I did not find a published biography, and did not confirm his relationship to other members of the Zevin family.
Torah work and communal duties. The Rebbe acknowledged that communal obligations and publishing Torah works can be overwhelming, but encouraged perseverance (IK 2342), and taught that spiritual growth is bound up with practical support for holy institutions (IK 7258).
Spreading Tanya. He encouraged active involvement in spreading the teachings of Tanya and in celebrating Yud-Tes Kislev (IK 8254), and taught that increasing spiritual light brings blessing in physical matters as well (IK 8564).
Personal connection. The Rebbe valued direct communication and personal connection over indirect updates (IK 8494). In an early letter he clarified a misunderstanding about a charitable donation (IK 721).
Sources: the Rebbe's letters cited above.