As Andy was saying, yes it depends. Both are correct in their own context, so generally speaking the Preterite will be used for completed actions in the past and/or a specific time in the past while the Imperfect is generally used for continuous actions, or habits in the past. The lesson you were seeing is one for just the conjugation so we didn't put any enphasis on time phrases or usage. There are more specific lessons of usage (for both tenses) coming up soon.
Not under all circumstances. You're talking about the difference between the El Pretérito Imperfecto (yo tenía) and the El Pretérito Indefinido (yo tuve). The former is used to denote things that were happening in the past or used to happen; the latter things that are completed.
A couple of links (one here, one elsewhere):
Andy, I think you were referring to this specific lesson about Pretérito Perfecto vs Pretérito Indefinido.
Here is the link:
FYI, you can find related lessons via the tags at the top of the lesson and any links within the lesson text. These take you to pages that list all of the lessons, so for example you could navigate either via tense name, then scroll down the list, you'll find all related lessons including all the usage lessons.
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