Learn Italian: Il gatto è sotto il letto.

While many location phrases need an extra preposition like a or da (for example, vicino a or lontano da), sotto (under) and sopra (on top of) are exceptions. They usually connect directly to the noun and its article, without needing an extra connecting word.

Does sotto ever combine with the article il to make a single word, like nel or sul?

No, sotto never merges with definite articles. Unlike su + il = sul or in + il = nel, you will always keep sotto and the article as two separate words: sotto il.

Could I use sta instead of è here, since it describes where something is located?

It is much more natural to use è (from essere, to be) to state the simple location of an object. While the verb stare is sometimes used for location in certain regional dialects, standard Italian prefers essere to say where things are.