it is water vapor
Condensed water droplets held suspended in the air are known as fog. Fog forms when the air near the ground becomes saturated with water vapor, causing the water vapor to condense into tiny droplets that linger in the air.
The amount of water vapor that air can hold depends on its temperature. Warmer air can hold more water vapor than cooler air. This relationship is described by the concept of relative humidity, which is the ratio of the amount of water vapor present in the air to the maximum amount the air could hold at that temperature.
It depends were you are, generally it would stay colder if you left it in the water
Warm air. It's denser and can therefore hold more than cool air.
Yes, it is true.
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Assuming the glass cup held a cold liquid, the air closest to the cup will be colder than the surrounding air, causing water vapour in the air to condense into liquid water droplets.
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When a balloon is held in hot water, the air inside the balloon heats up, causing the air molecules to move faster and spread out. This increases the pressure inside the balloon, pushing against the flexible walls and causing the balloon to inflate.
Humidity means amount of water vapour present in air with respect to total amount of air. Relative humidity means ratio of amount of water vapours per unit volume of air to the capacity of air to held maximum water vapours in unit volume of air, at given air temperature.