The following is from my personal knowledge and understanding which could be faulty.
Regarding the "...scholars are unanimously agreed that a Muslim who insults the Prophet (peace and blessings of Allaah be upon him) becomes a kaafir and an apostate who is to be executed." The punishment was judged because of the Muslim's apostasy and
not because blasphemy was unanimously considered a capital offence. The issue of apostasy is a different subject discussed at some other place on this forum.
Regarding the woman who was strangled and no blood money was prescribed for her murderer, although this is, as far as I know, the
strongest evidence for prescribing the capital punishment, it still falls short because of the fact that nowhere in the narration, is the Prophet or the companions commanding the punishment. The incident happened and the issue was what is to be done now, not whether the incident was right or wrong.
I haven't come across the opinions of critics regarding the Sunan al-Nasaa’i narration and not being a scholar I will try not to make any conclusions on it, although I
do have reservations on deriving
Sharia commands, especially as significant as
Hadd punishments, from such indirect events.
Regarding, "It may be noted from this that the Prophet (peace and blessings of Allaah be upon him) had the right to kill whoever insulted him and spoke harshly to him, and that included both Muslims and kaafirs." in my humble opinion, this is a fallacious (
non-sequitur) conclusion.
Regarding the Sa’d ibn Abi Waqqaas event, this event is used to support the death penalty for both apostasy and blasphemy. Supporters of the death penalty believe that apostasy and blasphemy are part of
Sharia as
Hadd punishments i.e. their punishment cannot be lessened, divinely ordained by God, it has to exist until the day of judgement and no one can ever be pardoned from this punishment. Critics use this same narration to argue against the
Hadd status of these crimes, by pointing out how the Prophet clearly forgave those crimes. The supporters, from their point-of-view, resolve this discrepancy by arguing that Prophet Muhammad had the special God-given right to forgive even
Hadd punishments. Critics do not accept this understanding.
See the following links for a different understanding
even by some classical scholars,
www.dawn.com/news/1154856www.dawn.com/news/1149558defence.pk/threads/the-lies-of-the-clergy-on-blasphemy-and-295-c.99787/