What are constellations that follow the path of the sun?
These are the ZODIACAL CONSTELLATIONS - the constellations of the zodiac.
The path that the sun appears to take through the stars and other objects in the sky is the "ecliptic". The constellations lined up along that path are the constellations of the "Zodiac". There's no particular name for the path that the sun appears to follow around the earth. It does that every day, and the apparent path is slightly different each day.
How many constellations are there within the path of the sun in the sky throughout the year which also known as the zodiac?
The zodiac signs follow the apparent path of the Sun in the sky. To the ancient people the Sun was considered to the facilitator of all life. In astrology the Sun came to represent the native's self or ego, in its most basic expression. The sign the Sun was thus indicated the traits of that given persona.
Yes, as the Earth revolves around the sun and the seasons change, the constellations that were previously in the direction of the sun are now in the opposite direction of the sun, so we can see them at night. In other words, we can never see any constellations that are in the same direction as the sun, but as the seasons change the sun's direction changes.
No, you do not (in most places on Earth). As the Earth orbits the Sun, it is "in" different constellations during the course of a year. That affects the constellations that you can see at night. However, depending on your latitude, some constellations can be seen all year. That's because they are away from the path of the Sun in the sky and remain above the horizon all the time.