Learn Croatian: Osvijetli ključanicu svjetiljkom! - Illuminate the keyhole with a lamp!

Because svjetiljkom is in the instrumental case and represents the tool used to perform the action. In Croatian, when you use a physical object to do something, you use the bare instrumental case without the preposition s or sa. You only use s or sa to mean "with" for accompaniment, like doing something alongside a person.

Both osvijetli and svjetiljkom come from the same root word for light. Why does one use ije and the other je?

This reflects a common Croatian spelling rule based on syllable length. The root is svijet (meaning light). When the vowel sound in the root is long, it is spelled with ije, as in the verb osvijetliti. When the syllable becomes short because of added suffixes, the ije naturally shortens to je, as in the noun svjetiljka.

How is the word ključanica (keyhole) built?

It is derived directly from the word ključ (key). The suffix -nica or -anica is frequently used in Croatian to create nouns that represent a place or container for the root noun or verb. Here, it simply means the place for the key.

Why use the perfective verb osvijetli for this command instead of an imperfective verb?