Too vague a question. If you mean, does sealing the cup change the mass, then no it does not change the mass of the water, though the sealing material would add its own mass to the total.
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Yes, the mass of the sealed cup of water would remain the same as long as no water is added or removed from the cup. The mass is a measure of the amount of matter in the system, which would not change in a sealed environment.
After water has been boiled, its mass will stay the same.
Yes, all samples of pure water have the same mass because the mass of water is determined by its chemical composition, which consists of two hydrogen atoms and one oxygen atom. This means that regardless of the volume or container, the mass of pure water remains constant.
Need more data to answer. Are you talking about the mass of an object, neither air nor water, being the same when in the air or in the water? Yes. Are you talking about the total mass of all the air on earth compared to the total mass of all the water on earth? Definitely not.
The density of water remains constant regardless of the volume or shape of the container it is in. This is because the mass of water and its volume stay the same, resulting in the same density for both a pool and a cup of water.
Yes, when water evaporates, its mass does not decrease. The water molecules simply change from a liquid state to a gaseous state, but the total mass of the water remains the same.