Home electrical transmission question
AC current is sine wave with 60 hz frequency.


No, the AC supply is sinusoidal voltage. The current waveform depends on the load but for resistor loads it will also be sinusoidal.


  ... how is this helpful in understanding electricity and transmission? 


It's not sinusoidal to help with understanding. It is sinusoidal because we use rotary generators and the voltage output alternates positive and negative in a sinusoidal fashion as the magnets pass the coils.


  Does the sine wave progress through electric wire or stands static and oscillates?


The alternating of the current is more like a bicycle chain oscillating back and forth a bit. The chain moves very little but the effect is felt immediately at the other cog wheel.


  When electricity enters the house through hot wire and is consumed by electronics, the neutral wire takes the unconsumed electrons back to sub station. 


"Electricity" doesn't enter the house. Current does.

Current flows in a circuit - again like the bicycle chain. The number of links in = the number of links out. When you are pedaling your bike you don't "consume" the links. Current from the power station returns to the power station through the load.


  Why is this [the neutral] simply grounded? 


So that we only have to fuse one wire - the live. Since the neutral has been "neutralised" there is little voltage on it and no fuse is required.


  Is it not wasting electricity? 


No.


  Can't the electrons be harnessed?


Don't think of electrons. Think of current. If you try to use the current in the neutral you will cause a voltage drop on the neutral wire and the voltage available to the original load will drop - possibly causing a malfunction.

You need to study basic electrical theory some more.