Question

Which igneous rock is fine-grained and have a lot of pyroxene?

Answer 1

That would be basalt (https://en.wikipedia.org/wiki/Basalt), a major portion of our oceanic crust.

Explanation:

Basalt consists of calcium-rich plagioclase feldspar combined with "mafic" (magnesium-iron or magnesiun-ferric) silicate minerals like pyroxene. This composition makes basalt denser than rocks such as granite we see in our continental crust.

The rocks with the most pyroxene in them are the ultramafics (lomatite) wherein pyroxene can be up to 50% of the rock (see pic).

In addition to the crust on our ocean bottoms, basalt is seen on the Moon and Jupiter's volcanically active moon Io.