Learn Italian: Non è un caso grave. - It is not a serious case.

Grave belongs to a group of Italian adjectives that end in -e in the singular for both masculine and feminine nouns. So, you say un caso grave (masculine) and una situazione grave (feminine). To make it plural, the -e changes to -i (casi gravi).

Could I use the word serio instead of grave here to mean "serious"?

You can, but grave is the most natural choice for medical conditions, accidents, or mistakes to mean "severe." Serio is more often used to describe a person's personality (earnest, not joking) or a work-related matter.

Where is the word for "it" in this sentence?

Italian usually drops subject pronouns like "it" because the verb itself gives enough information. Here, the verb è (is) stands alone, and we naturally translate it as "it is" based on the context.