Is what was said about advising a Christian friend regarding her father-in-law, who converted to Islam and then ostracized his family, considered "backbiting"? And does embracing Islam mean ostracizing one's family?

Backbiting is not considered tale-bearing when conveying speech between people with the intention of reconciliation. Similarly, backbiting (ghibah (definition)) only occurs when a Muslim is mentioned in a negative way in their absence. It is not permissible to abandon disbelieving relatives; rather, one should maintain ties with them, treat them kindly, and show them the virtues of Islam, while avoiding any harm that might result from such interactions.