Sanhedrin 13: Seasons in Their Time

What happens to the equinox, when calculating the calendar? Is it considered the beginning of the new season or the end of the old season? The equinox is significant as it is a marker for the seasons falling as they should, in the given months, with a focus on the autumn at this time. As for the spring, if the winter season extends 19 days into the Nisan season, that is enough to intercalate the year. Also, "semikhat yadayim" -- the laying on of hands from elder sages to up-and-coming sages as the means of conferring authority, which requires 3 judges (but why does it?). Plus, the authority to levy fines, and how the details of them were preserved.