Learn Swedish: Jag packade väskan på kvällen. - I packed the bag in the evening.

Packade comes from the verb packa (to pack). Because packa is a regular Group 1 verb, it ends in -a in its base form. To create the past tense, you simply add -de to the end, giving you packade.

Why does the sentence use väskan (the bag) instead of min väska (my bag)?

When it is obvious that you are talking about your own belongings or body parts, Swedish prefers to use the definite form, like väskan. While min väska is grammatically correct, using väskan sounds much more natural here.

Why is it på kvällen instead of using a preposition like i for 'in the evening'?

Swedish uses the preposition på plus the definite form of the noun for general parts of the day. So, 'in the morning' is på morgonen and 'in the evening' is always på kvällen.

Do native speakers fully pronounce the -de at the end of packade?

In everyday spoken Swedish, the -de ending on Group 1 verbs is very often dropped, so packade sounds exactly like packa. You have to rely on the context to know it happened in the past, but you must always write the full -de.