Q 1: Regarding the Athar (narration from a Companions) which reads:
"The Mu'adhin (caller to Prayer) is in charge of Adhan (call to Prayer) and the Imam (the one who leads congregational Prayer) is in charge of Iqama (call to start the Prayer)";
does this Athar just mean that the Imam is the person to decide the time of Iqamah or does it mean that the Imam is entitled to ask a person other than the Mu'adhin to make Iqamah?
The narration quoted in the question means that it is the Imam who decides the time of Iqamah. The concerned narration does not imply that the Imam is to ask a person other than the Mu'adhin to make Iqamah without there being a legal excuse, for doing so contradicts Sunnah (whatever is reported from the Prophet). A Hadith that supports the foregoing is what is related by
Abu Dawud and
Al-Tirmidhy from the Prophet (peace be upon him) that he said:
Whoever calls the Adhan pronounces the Iqamah.
Al-Tirmidhy commented: "The fact that most scholars accepted such a Hadith and acted upon it is a sign of its authenticity."May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.