1) Yes. Venus does undergo retrograde motion when viewed from an outer planet. This occurs as Venus overtakes the slower moving world, causing the line of sight between it and the outer world to change direction against the background stars.
2) Make sure the box labeled "Sun" is checked. The Interactive then clearly shows that, when viewed from the Earth, Venus always appears close to the Sun because its orbit is smaller than the Earth's. As Venus completes its orbit it first swings from one side of the Sun to the other in the Earth's sky. Thus it appears either during Sunset or Sunrise when the sky is dark enough for Venus to be visible.
3) When an inner planet passes an outer one, their separation is relatively small compared to when they are at opposite sides of the Sun. Thus you would expect a planet undergoing a retrograde loop to brighten in the sky or appear larger when viewed through a telescope.
4) From a physical standpoint, it was pretty hard to imagine that Earth was moving through space and in orbit around the Sun. Our senses tell us that it is the Sun and all the planets that go around the Earth, while the Earth feels quite stationary to us. Also, long-held beliefs are not easily changed, and the Earth-centered view initially proposed by the Greeks had been the accepted model for many centuries. During this period, the Catholic Church reinforced this by holding that belief in the heliocentric model was heresy. The seeds of the Protestant reformation were growing as well, and so astronomy became part of larger power struggle in Europe at the time.