Shape Water only allows you to select one effect per casting, and to have two of its its non-instantaneous effects active at any one time. It affects water that fits into a 5-foot cube. Casting it takes an action, so you normally can only cause one effect per round. To your quesitons
1. Can you create an iceball to drop from 30 feet in the air? No.
The first effect that you can cause is:
- You instantaneously move or otherwise change the flow of the water as you direct, up to 5 feet in any direction. This movement doesn’t have enough force to cause damage.
As you can move water "in any direction", you conceivably could move the 5-feet per side cube up 5 feet. However, since the movement is limited to 5 feet in any direction, you cannot move it higher in one casting. The effect is instantaneous, it does not change the water magically to continue floating -- once you moved it up, the water's weight will make it drop down again. Instantaneous means (p. 203, PHB)
The spell harms, heals, creates, or alters a creature or an object in a way
that can’t be dispelled, because its magic exists only for an instant.
So there is no way you can move the water up 30 feet by repeated castings of the spell. Each time you cast it, it moves up 5 feet, then drops down again. By the time you can cast the spell again a round later there is no floating body of water in the air.
2. Can you create an opaque, moving 10-feet dome of water? No
The third bullet allows you to:
- You change the water’s color or opacity. The water must be changed in the same way throughout. This change lasts for 1 hour.
So you could change a block of water to be opaque as the first effect. The second bullet then allows you to:
- You cause the water to form into simple shapes and animate at your direction. This change lasts for 1 hour.
Consensus by this answer is that simple shapes formed could be larger than a 5-foot cube, and a dome would be a simple shape. I'm not convinced of this. The spell says "You choose an area of water that you can see within
range and that fits within a 5-foot cube." so the area of effect here is water that fits within a 5-foot cube. Even if you can form simple shapes with the water, that does not change the area: they still must fit into a 5-foot cube.
But lets assume your DM rules the other way, because there is an upvoted answer for that. Then you could create a dome out of the opaque water with the second effect. (It would not work the other way round, because if you form the dome first, it does not fit into the are of water you can affect to make it opaque any more).
However, you then have used up both your effects. The question is if you could move the water around, because it is "animated"? I think that cannot be the intent, because it would invalidate the first effect bullet, which lets you move the water around: that bullet would be useless, as you instead could just declare your simple shape is a 5-foot cube, and move the water around in any way or distance you want.
And you also cannot move the dome with the instantaneous movement effect, because it is larger than the 5-foot cube you can affect.
So, even if you could create the opaque dome (which I think you cannot), you cannot have it move around.
3. Can you make ice weapons out of the water? Yes
See this Q&A. You can form the shapes with the first effect use, and freeze them to be ice with the second. But they will only be as good as your DM thinks weapons made from ice will be. The same goes for gears or other simple shapes. (It is up to your DM to decide if a gear still qualifies as a "simple" shape).
