If there's 1 gram of nitrogen (N2) at 1 L and 1 gram of hydrogen (H2) at 1 L, would the pressure of H2 be greater than the pressure of N2? And would the density of H2 = the density of N2 at these conditions?

There would be more moles of H2 than N2, but the same mass and volume, so I think the answer is yes to both questions, but I wanted to make sure.

the masses and volumes are the same, so the densities would be also

there are more moles of H2, so it has a higher pressure

just as you surmised