Learn Croatian: Nikada ne kupujem jeftinu šminku.

Because the sentence describes a general habit. In Croatian, words denoting habitual or repeated frequency, like nikada (never) or uvijek (always), strongly trigger the use of imperfective verbs. You are describing the ongoing state of your habits, rather than a single completed action.

Is it strictly necessary to use double negation (Nikada ne...) in this sentence?

Yes, it is mandatory. Unlike in English, Croatian requires negative concord. Whenever you use a negative pronoun or adverb like nikada (never), nitko (nobody), or ništa (nothing), the verb must also be negated with ne.

Is there any difference between nikad and nikada?

No, they mean exactly the same thing. The final -a in nikada is an optional vowel. Speakers often drop it or keep it based on the rhythm of the sentence, the sounds of the surrounding words, or simply personal preference.

Can I change the word order to Ne kupujem nikada jeftinu šminku?

Yes, that is perfectly fine. Placing nikada at the very beginning of the sentence puts a bit more rhetorical emphasis on the word 'Never' for dramatic effect, but both word orders are very natural and grammatically correct.