Bismilla hir rahman nir raheem
As sallamu alaykum wa rahmatullah wa baraktuhu
May allah have mercy on me and you and all those who will read this.
Islam does say how the goverment and country should run, and none of the four above is what islam promotes and islam rejects that the majority rules what should be halal or haram for the society even if it is against what allah loves which is called democracy, this is a quick response to your three questions.
For a more detailed response.
Q1) allah says to the prophet muhammad صلى الله عليه وسلم who was the ruler in surah 5vs49 “And so judge between them by what Allaah has revealed . . .”
And in same verse and follow not their vain desires . . .” [aayah 49]
Why is this evdidence it is because it is also aimed at whoever assumes role of leadership .
Allah says in surah hadid on last page surah57vs 25
"Certainly We sent Our Messengers with clear proofs and We sent down with them the Scripture and the Balance that may establish the people justice".
This strengthens what i previously mentioned because allah says "so mankind can judge". So any muslim government has to rule.by quran sunnah upon understanding of the sahabah.
In regards to the way things are run, it is of two types that which is restricted to the evidences and that which the ruler has freedom to choose what he sees fit for his people such as cars,airplanes etc. Everything in worship is haram until proven halal, but all wordly issues are halal until proven harram. And judgements in inheritance, etc is from acts of worship and building roads, etc is from wordly issues worship here doesn't just me salah. And one can look into how sahabah run their states for guidance.
Q2) none of the four is what is encouraged.
The way it should be is how the companions after death of prophet done things which is one khalifah and he appoints the governers for each land and the khalifah is voted in by the people of power and influence or he comes into power by being appointed by current khalifah or he takes power by force.
There should never be more than one overall ruler hence abu bakr was sole ruler then umar etc. This isnt an dictorship because this khalifah rules by book of your lord which is most just and you obey him in that which is good.
- Democracy is disbelief in allah and his messenger because a person is making the society the criterion for whats halal or harram. Allah says
Or have they partners with Allaah , who have instituted for them a religion which Allaah has not allowed?” [al-Shooraa 42:21]
Partners here can mean you make the people like Allah in that they say whats the religion and is not. Religion also means way of life.
"Have you seen those who claim that they believe in that which has been sent down to you, and that which was sent down before you, and they wish to go for judgement to the Taaghoot (false judges, etc.) while they have been ordered to reject them" [al-Nisaa’ 4:60-61].
The Hukm (Legislating, Commands, Judgment) is for none but Allah. "He has commanded that you worship none but Him, that is the (true) straight religion, but most men know not.” [Qur’an Chapter 12: 40]
Imam al-Baghawi (died 509AH) commented on Quran Chapter 12: 40 in Tafsir ul-Baghawi, Vol2, Pg. 427, saying, “Indeed the (Right of) ruling, commanding and prohibiting is for none but Allah".
And Allah knows best.