How long does Earth take to orbit the Sun?

About 365.2422 days, and every calendar problem in history comes from that fraction. Ignore it and the seasons drift; the Julian calendar's leap day every fourth year overcorrected by about eleven minutes a year, which had accumulated to ten days by 1582 and forced the Gregorian reform - no leap year in century years unless divisible by 400.

There is more than one kind of year, which matters more than it sounds. The sidereal year is one orbit measured against the stars. The tropical year, which is what calendars track, is measured equinox to equinox and is about twenty minutes shorter, because the Earth's axis slowly precesses like a spinning top over 26,000 years. Track the wrong one and the seasons wander round the calendar over a few thousand years.

The orbit is also not a circle, and the Earth does not move at a constant speed round it - it moves faster when closer to the Sun in January, which is Kepler's second law. Northern winter is therefore a few days shorter than northern summer, and the seasons are not equal in length.