Our calendar months do not coincide precisely with the actual celestial month. We are out of sync by a little bit of time (hence, Leap Year). This means that the Sun moves into a new zodiac sign approximately every month, anywhere between 19th and the 23rd of our month. That group of days is called a cusp, meaning the span of days in which the Sun may change sign. However, being born during those days does not automatically mean that you have two Sun signs. That is a common misconception. Birth charts are calculated using astronomical ephemerides that track the exact time of a Sun sign change for every year. If you were born between the 19th and 23rd of any month, you must check an ephemeris to see exactly where the Sun was at the time of your birth.
No, they aren't. There's actually two different kinds of systems used for Western astrology, neither one of which is strictly fixed to the Gregorian calendar; one fixed to the vernal equinox and the other fixed to the positions of the fixed stars (there are many variations on the latter.)
Because the Gregorian calendar (and the same is true of any regular solar calendar) has very little variation in regard to the vernal equinox, in that system dates fixed to the Gregorian calendar are approximately correct and are common in casual use with regard to the most common astrological period referenced, the zodiac signs.
https://en.m.wikipedia.org/wiki/Sidereal_and_tropical_astrol...
https://www.today.com/popculture/your-life-lie-zodiac-has-ch...