星期天

English says on Sunday, so learners add 在 out of habit. Chinese time words like 星期天 usually go straight before the verb. 我星期天去 is the normal everyday pattern. 我在星期天去 is not wrong, but it sounds like you are stressing that exact Sunday. In a casual WeChat plan, drop 在 and keep the time before the verb.

Both mean Sunday, but they live in different rooms. 星期天 is the everyday word you use with friends, family, and coworkers. 星期日 sounds more formal, so it shows up in schedules, notices, and official writing. You will also hear 礼拜天 in casual northern speech, but keep it out of formal writing. For HSK 1, learn 星期天 first.

星期 by itself means week, not Sunday. If you say 上个星期, you are talking about the whole previous week. Add 天 to point at one specific day, Sunday. That is why the story says 上个星期天 when the speaker remembers a past Sunday. Drop 天 and the meaning shifts from a day to a week. “我：“上个星期天，你说你喜欢他们的那个桌子和那个电脑椅。” (I: 'Last Sunday, you said you liked their table and that computer chair.') ── [《吃的东西和喝的东西》](/read/buying-food-drinks#s15)