Questions & Answers about Я должен собрать свой чемодан.
Why use свой here instead of мой for 'my'?
Свой is a reflexive possessive pronoun that refers back to the subject of the sentence. Because the subject 'I' (Я) is acting on an object that belongs to 'I', Russian prefers свой (meaning 'one's own'). While мой чемодан isn't strictly wrong here, свой is much more natural and common.
Why didn't свой чемодан change its ending? Isn't it the direct object?
It is the direct object, so it is in the Accusative case! However, for masculine inanimate nouns (non-living objects like чемодан), the Accusative form looks exactly the same as the Nominative (dictionary) form. The pronoun свой simply copies the noun's case and gender.
Is должен a verb, and does it change depending on who is speaking?
Does the verb собрать always mean 'to pack'?
Not exactly. The core meaning of собрать is 'to gather', 'to collect', or 'to put together'. When you talk about a suitcase (чемодан) or a bag, you are gathering your things into it, so 'to pack' is the best English translation for this specific context.