Learn Hardcore Russian: Нижний ящик пустой.

Ящик ends in a consonant, so it is a masculine noun. It is the subject of the sentence and therefore in the nominative case (singular). Both adjectives — нижний and пустой — agree with ящик in gender (masculine), number (singular) and case (nominative), hence the endings -ий on нижний and -ой on пустой.

Why isn’t there a verb like есть (to be) or is in this sentence?

In Russian, the present-tense form of the verb быть (to be) is normally omitted. The full idea “The bottom drawer is empty” is conveyed simply as Нижний ящик пустой, with the copula есть understood but unspoken.

How can I tell if this means “a bottom drawer” or “the bottom drawer” without articles?

Russian does not use articles like a or the. Whether you interpret Нижний ящик пустой as “a bottom drawer is empty” or “the bottom drawer is empty” depends entirely on context (what you already know or have mentioned).

Where is the stress in Нижний ящик пустой, and how do you pronounce it?

Stress falls on the first syllable of нижний (НИжний), the first of ящик (Ящик), and the second of пустой (пустОй). A basic phonetic rendering is [ˈnʲiʐnʲɪj ˈjaɕɪk pʊˈstoj].

What’s the difference between the full form пустой and a short form like пуст? Can I say Нижний ящик пуст?

Full-form adjectives (пустой) can be used both before a noun and as a predicate after it. Short-form adjectives (пуст) are only predicative and often feel more formal or literary. You can say Нижний ящик пуст, but in everyday speech Нижний ящик пустой is more common.

Can I change the word order? For example, пустой нижний ящик or ящик пустой нижний?

Russian allows some flexibility, but typical simple statements use: attributive adjective + noun + predicate adjective.

пустой нижний ящик would be read as “the empty bottom drawer” (both adjectives attributively before the noun).
ящик пустой нижний is ungrammatical.
If you tried нижний пустой ящик, it would sound awkward and mean “the bottom empty drawer” (two attributive adjectives in a row), which is unusual.

Why нижний ящик and not низкий ящик if I mean “low drawer”?

Нижний means “lower” or “bottom” (position in a stack or series). Низкий means “low” in height. Since you’re referring to the drawer’s position (it’s the bottom one), you use нижний ящик. Saying низкий ящик would imply “a drawer that is short or not very tall.”