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Try the mathematics and you will see how.For f(x) = ∫x dt, where x is a square wave function, f(x) will be a triangle wave function.Also try what happens where x is a triangle wave function!
A sine wave has no harmonics. It only has a fundamental, so the value of the 2nd, 3rd, and 12th harmonics of a sine wave is zero.
It's called a sine wave because the waveform can be reproduced as a graph of the sine or cosine functions sin(x) or cos (x).
The fourier series of a sine wave is 100% fundamental, 0% any harmonics.
Since a sine wave is described by the trigonometric sin(x) function, which is symmetrical, the sine wave is also symmetrical, unless there is a DC bias, in which case it is not. (It depends on your definition of symmetry)