Work done on the system.
Yes, you are doing work on the water.
An adiabat. Consider adiabatic compression: work is done on the gas and the process is too fast for any heat transfer, so the energy of the gas increases. Therefore the temperature must increase. Moving from a lower T isotherm to a higher T isotherm as V decreases makes a steeper curve than the isotherms themselves.
Very slow processes are isothermal, because then there is enough time for heat to flow until the temperature equilibrates with the surroundings.
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