Question

Why do giant stars have much more narrow lines than main-sequence dwarfs?   Why are the stars that do not show
strong H Balmer lines either have either very low or very high surface temperatures?

Answer 1

Those characteristics depend mainly on a star's mass.
Most stars would start consisting mainly of hydrogen-1.
After a while, they burn up that fuel, and have more helium-4.
Later they can create heavier elements (the so-called "metals").

The color of a star depends almost entirely on its surface temperature.
The hottest stars are blue or bluish white in color.

(The star's chemical composition only affects the narrow "absorption" lines in the otherwise continuous spectrum.)

For "Main Sequence" stars that temperature is closely related to the star's mass.
Also the size is related to mass.
So, in simple terms, more mass means higher temperature and size.
Most stars are Main Sequence stars, but many are not.

Things for those other stars are more complicated.
Color and temperature are still closely related. However, color and size are no longer related in a simple way.
For example, a red giant star is much larges than a red dwarf star, but has a similar surface