The first day of the seventh month is the "new year of years." It is the anniversary of the Sixth Day of Creation and of Adam and Eve's creation. Years are numbered from the seventh month, as is evident in the instructions concerning the shemitah and yovel years, which are dated from the seventh month, not the first month.
The first month (Nisan) is the new year of the seasons, the new moons, the Biblical feasts, and the reign of Jewish kings. The intercalation is made prior to the first month, which fixes the months and seasons for the year to come. But years (such as the shemitah and yovel mentioned above) are still dated from the seventh month, which is when the year itself changes.
That is a tradition. It is not in the Tanakh.
It is the anniversary of the Sixth Day of Creation and of Adam and Eve's creation.
That is a tradition. It is not in the Tanakh.
Years are numbered from the seventh month, as is evident in the instructions concerning the shemitah and yovel years, which are dated from the seventh month, not the first month.
You are correct that the Talmud Yerushalayim Tractate Sheviis records the Mishnaic ruling that the Shemitta year (and therefore Yoveil) begin on Rosh Hashannah. However, that ruling falls afoul of Devarim 31:10-11 which goes completely unmentioned through several chapters of discussion on the topic:
Although there are exculpatory reasons for it, the ruling to which you refer (on page 1b if I recall correctly) is clearly in conflict with Torah. As I said, there had to be an exculpatory reason. Care to know why they did it?
A limited release of my book on Shemitta is available here. It is undergoing a major revision that will be placed online for free. Here is a review.