It was a time when Jews (primarily) and hypocrites were hell-bent on harming Muslims and their favorite target was Muslim women for they were vulnerable. Situation was so grave that even one Muslim woman was raped. It was all happening during dawn and dusk, two times when women use to go out to answer the call of nature. When Jews were prosecuted that used to say, O well, it was dark and we did not recognize them, we thought they belonged to our tribes, or were our slaves girls etc. Such were the circumstances when these ayahs came.
Please note down,
orders are not general but for specific times, dusk and dawn and in a situation where Jews were stalking on Muslim women.
Now, I'll explain the 5 ayahs one by one:
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And those who harm (yu'zoona) momins and mominaat without any reason have certainly born upon themselves a slander and manifest sin.
Basically, Allah is warning the Jews and hypocrites for slandering and harming Muslims. Next Allah says ...
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So O Prophet (PBUH), tell your wives and your daughters and the women of the believers to bring down over themselves their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.
So basically Allah is asking the Prophet (PBUH) to ask Muslim women to cover themselves such that thry can be recognized in relatively dark times of dusk and dawn so that Jews and hypocrites would no longer be able to give the excuse that they did not recognize them. Next Allah says ...
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If the hypocrites and those in whose hearts is disease and those who spread rumors in al-Madinah do not cease, We will surely incite you against them; then they will not remain your neighbors therein except for a little.
That even after taking the precautionary measures described in earlier ayah, if the hypocrites and Jews do not stop from causing harm to Muslim women, Allah will order the Muslims to punish them. Next Allah say ...
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Accursed wherever they are found, [being] seized and massacred completely.
And the punishment will be to kill them wherever they are found.
Now if we read ayah from 58 to 61, it is very clear that Muslim women are asked to cover themselves up (no mention of face, head, hairs, veil and Arabic has words for all these articles BTW) so that that Jews or hypocrites who were finding excuse to harm them, while they go out in secluded places to answer the call of nature, could no longer be able to do that. Even after that, if they continued to harm Muslims, Allah will order Muslims to punish them with death.
That is all and Mullah have made a mountain out of a molehill.