At the end of his comment on https://blog.nli.org.il/en/danny-kaye/ Barry Steinhart writes “one doesn’t write ז״ל on a woman and especially a secular one”. Is either statement correct?
I am not familiar with this site, so I can’t vouch for anything that it say on it. It is true although the minhag for some reason is that men have the words זכרונו לברכהwritten after their name, and women it is עליה השלום. If someone wants, he may say זכרונה לברכה for a woman. Regarding the other point I don’t know, but it may depend on the circumstances.
Pesokim Uteshuvos Y:D 340-35. See ftnt. 320 that numerous gedolim wrote lezrona levracha on their mothers.