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Yes, of course. Rearrange the ideal gas law into the form $$\frac{P}{T} = \frac{nR}{V}.$$ Since by construction the volume and number of moles is fixed, the right-hand side of the equation is constant, so the pressure increases linearly with the temperature in your situation.


Objects don't feel temperature, even if it records temperature. But it would not "adjust" to the new temp and therefore feel cold if brought down to still above room temperature.


Your major confusion may be thinking intensive property must be property of material. There are 3 types of quantities, depending how they are related to system scalability: Extensive properties are additive wrt(with respect to) the system scaling. If there is twice as big system, there is twice as big value of an extensive property. Examples are mass, ...


The question was poorly designed with incorrect choices. Density is also intensive property. Density of 1 kg of water is same 0.001 gram of water so your answer is also correct. I feel the source of your confusion is between heat and temperature. This concept has bewildered big physicists and philosophers in the 18- and 19-century, so no need to feel bad ...

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