the horizontal component of a projectile moving with initial velocity of 500 m/s at an angle 60° to x-axis is equal to:
Don't confuse the terminology. Horizontal and vertical components are properties of vectors. Projectiles are not vectors.
it has to travel through the atmosphere, a bullet starts to slow down as soon as it leaves the muzzle, affecting the path of its flight.
Learn to crawl before walking -- almost all projectile motion studies begin in the absence of friction of any kind. That comes later, and even then it is simplified and ignores other factors that real-world long-range projectile motion problems have to take into account.