1)Under ideal conditions, if 300 J of work are required tolift a mass to a certain height, the same mass should provide ___ J to do work as it falls back to Earth.

Can you please comment as to whether my answer of 300 J is correct?

2)___ is conserved during an inelastic collision, although kinetic energy decreases.

I think it is energy, but is that specific enough? or are they looking for momentum?

1) 300 J

2) Momentum

Since the collsion is inelastic, kinetic energy is not conserved.