Is it permissible to say "Fatimah Az-Zahra, peace be upon her" or "Hussein, peace be upon him"?

Praying upon others besides the prophets, when done in conjunction with them, is permissible by consensus. However, when done individually, it is a point of contention:

The majority view is that it is impermissible, while Ahmad and most of his companions held it to be permissible, as long as it is not adopted as a شعار (slogan or distinguishing mark).

The correct view is that it is permissible, unless it is adopted as a شعار for a specific person, in which case it is impermissible.

As for singling out a person with the salutation of peace (السلام):

A group, including Abu Muhammad al-Juwayni, disliked it and prohibited saying "عليه السلام" (peace be upon him) for Ali.

Others differentiated between it and prayer (الصلاة), saying that peace is prescribed for every believer, living and dead, present and absent, and it is the greeting of the people of Islam.

It appears that singling out a Companion with the phrase "عليه السلام" is easier than singling them out with the phrase of prayer. Its mention has appeared in Sahih al-Bukhari, and there is no harm in saying that for Fatimah (may Allah be pleased with her) or other Companions, as long as it is not adopted as a شعار for the people of innovation.