• 课：a session on a subject
• 话题：topic
• 题目：a question (on a test paper. Your dictionary probably assumed you meant subject as in title, such as that in an Email.)
• 科目、学科：subject (as a discipline), with 科目 being a bit elementary, and 学科 being more advanced.

So 科目 probably fit your 2 scenarios best.

• 课（also 课程）：a session or a series of sessions on a subject
• 话题：topic
• 题目：a question (on a test paper. Your dictionary probably assumed you meant subject as in title, such as that in an Email.)
• 科目、学科：subject (as a discipline), with 科目 being a bit elementary, and 学科 being more advanced.

So 科目 probably fit your 2 scenarios best.

Related note: 门，as in 八门课程，etc.

• 课：a session on a subject
• 话题：topic
• 题目：a question (on a test paper. Your dictionary probably assumed you meant subject as in title, such as that in an Email.)
• 科目、学科：subject (as a discipline), with 科目 being a bit elementary, and 学科 being more advanced.

• 课：a session on a subject
• 话题：topic
• 题目：a question (on a test paper. Your dictionary probably assumed you meant subject as in title, such as that in an Email.)
• 科目、学科：subject (as a discipline), with 科目 being a bit elementary, and 学科 being more advanced.

So 科目 probably fit your 2 scenarios best.