Obviously all those assumptions are made since none of them have anything to do with the earth's rotation or its movement through space. That is how you test anything, by keeping all the unrelated/external variables constant. Otherwise the probability of the ball landing a little to the west (against Earth's rotation), North, South or East of the launching point is exactly the same. When tasting a teaspoon of sugar you wouldn't mix it in a kilogram of coffee powder and then declare that the teaspoon of sugar is bitter not sweet.
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1) Obviously it is. We are testing the effect of Earth's rotation and movement on a lofted object. I even said perfectly vertical. Introducing a horizontal force would end the experiment in a great big bowl of stupidity.
2) air/atmosphere/external force/internal forces have nothing to do with the Earth's rotation or movement and hence will always be kept constant, ideally at zero (except for gravity) in any credible experiment. The atmospheric pressure and air resistance will have no effect on the experiment whatsoever and I have no idea what you meant by the internal forces; the molecular forces in the ball will have nothing to do with the experiment.
3) The uniformity of gravity will not have any effect on a ball tossed vertically. On a moving missile the absence of uniformity in gravity will have the same effect on the missile whether its launched eastwards or westwards i.e. has nothing to do with the Earth's rotation and movement.
I still have no clue what your above post was about. Were we not discussing the effects or Earth's rotation and movement on a moving object?