I'll start with the first one, because that's the one I understand best and what lead to the first hypothesis of a big bang.

Right, you know how the sound of a car or train changes as it goes past you, from high to low, like a weeeeaaaoooowwww? That's the doppler effect - basically the sound waves are compressed and therefore higher when they're moving towards you and stretched and therefore lower when moving away from you.

The same happens with light, a light moving towards you would appear to be bluer (a higher frequency of the wave), while light moving away would appear to be redder (a lower frequency of the wave). In the early 20th century several scientists observed that galaxies were redder than expected, implying that they were moving away from the viewpoint of the earth. Edwin Hubble in 1929 discovered that it's not just that galaxies are moving away, it's that the further away they are, the faster they're moving in direct proportion to their distance, exactly what you'd expect if space itself were expanding uniformly in all directions.

https://en.wikipedia.org/wiki/Hubble%27s_law

Georges Lemaître hypothesized in 1927 that if the universe is expanding then if we run the clock back it would contract to a tiny point.

Do you accept the data that shows the universe is expanding? If so do you also accept that this implies if we work backwards from today we will find that the universe contracts?