Are the roots of these words from pre-Islamic days during which the Arabs would intercalculate days into the month, as Jews still do, before the Quranic verse which prohibited that?

Given that the months move back by 10 days each year, the names are historical and no longer relevant to the seasons, which shift now, no?

Another calender related question: is it incumbent on non-Arab Muslims to use this calender for other than religious purposes? What is the Shari’ah ruling on this?

In the Turco-Persian cultural sphere we have always used a different solar calender rooted in Iranian history, although dated beginning from the Hijrah after we adopted Islam, for day to day affairs. We only use the Islamic/Arab calender for religious purposes. Has any scholar ever discussed this?

But this is a lunar calendar! The months rotate over all the seasons of the year. How can any month be associated with cold/heat?

One is a feminine (Al-Uulaa) adjective, and one is the masculine (Al-Awwal) adjective for “the first.”

Any reason why is it Rabi’ Al-awal but Jamad al-Ula?