Learn German: Die Gegner sprechen schlecht übereinander. - The opponents speak badly about each other.

When a preposition like über (about) is used with einander (each other), they merge into a single compound word. This happens with almost all prepositions, giving us words like miteinander (with each other) or voneinander (from each other).

Could I just say über sich instead of übereinander?

You could, but it changes or confuses the meaning! If you say Die Gegner sprechen schlecht über sich, it usually means they are speaking badly about themselves. Using übereinander makes it crystal clear that they are doing it to each other.

Since Gegner doesn't have a plural ending, how can we tell it means multiple opponents here?

You have to look at the words around it. The article is Die (the masculine singular would be Der), and the verb sprechen has the plural -en ending. Masculine nouns ending in -er usually don't change their form in the plural.

Why doesn't schlecht have an ending here?

In German, words that describe verbs (adverbs) don't take any endings. Because schlecht describes how they speak, it stays in its base form.