How does different diffraction grating effect resolution and sharpness of lines in a line spectrum? In my lab notebook it asks us to think about the spectroscope further than the reading goes on.

It asks if we use a diffraction grating that contains 600 lines/mm in the spectroscope what do we expect would happen to the lines of the line spectrum in terms of sharpness and resolution.

Is the answer (assuming 600 is more than normal) that the lines would be both more sharper and have a higher resolution? My first thought was that the lines would be skinnier but more clear.
Sharpness is colloquial for how narrow a peak is. Resolution is how well we can see two features as they move closer together. You might do well to re-read your book to learn these definitions better. As already noted, skinnier and more clear have no meaning in spectroscopy.

A search on terms such as diffraction grating equation will give you further reading to support or invalidate the guess (hypothesis) that you propose.