Learn Italian: Questa mostra esplora il contrasto tra il vecchio e il nuovo. - This exhibition explores the contrast between the old and the new.

In Italian, you can turn an adjective into an abstract noun by putting the masculine singular definite article il in front of it. Here, il vecchio means the abstract concept of "the old" (or "what is old"), and il nuovo means "the new." This is a very common way to express abstract ideas.

If I wanted to refer to "old things" and "new things", could I just make them plural and say i vecchi e i nuovi?

No, because making these substantivized adjectives plural changes their meaning to refer to people. I vecchi would mean "the old people" (or old men), and i nuovi would mean "the newcomers." To talk about the abstract concepts of old and new, you must stick to the masculine singular il.

I learned the word mostro before. Is mostra just the feminine version of it?

They look similar but mean very different things! Il mostro means "the monster." La mostra, however, means "the exhibition" or "the display." It comes directly from the verb mostrare, which means "to show."

Could I use fra instead of tra for "between" here?