Learn Italian: Ho diversi mascara nel cassetto. - I have several mascaras in the drawer.

The meaning of diverso changes depending on where you put it! When it comes before a noun, like diversi mascara, it acts as an indefinite adjective meaning 'several'. If you put it after the noun (e.g., mascara diversi), it becomes a regular adjective meaning 'different' (as in, mascaras of different brands).

Since it says diversi, shouldn't the noun be plural too? Why is it mascara and not mascari?

It is plural! In Italian, foreign loanwords usually do not change their endings to form the plural. Mascara is one of these invariant words. You can tell it is plural here because of the plural adjective diversi right in front of it.

Why is it masculine (diversi) and not feminine (diverse)?

Most foreign loanwords adopted into Italian are treated as masculine by default. Since a mascara is an inanimate object without a natural gender, it simply takes this default masculine gender.

Why do we use nel cassetto instead of just in cassetto?

When talking about a specific physical location like a drawer, Italian requires the definite article. Nel is an articulated preposition, meaning it is the combined form of the preposition in plus the masculine singular article il.