Which of these are state functions: pressure, heat, work, internal energy, temperature, volume? …

The first law: $\Delta U = Q - W$. $Q$ is positive when heat goes into the gas; $W$ is positive when the gas does work on its surroundings, so work done on the gas is negative. For an ideal gas, $\Delta U > 0$ means it gets warmer.

The internal energy of an ideal gas is the kinetic energy of its molecules: $U = \tfrac{f}{2}nRT$, with $f = 3$ for a monatomic gas and $f = 5$ for a diatomic one. It depends only on the temperature, so $\Delta U$ is the same for every path between two states.