Is it permissible for a woman to say: "O my beloved one" when a specific companion is mentioned, like 'Umar, may Allaah be pleased with him, for instance?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

In general it is an obligation on a Muslim to love the companions and loving 'Umar in particular is also an obligation on each and every Muslim. Therefore, there is no harm for a Muslim man or woman to say: "O my beloved, such and such person" when 'Umar, or other companions are mentioned. This is nothing but expressing he love that is in the heart for this honourable companion and whoever loves a people, he will be resurrected with them.

Allaah Knows best.