1. Even though her buziness, she takes of her family very carefully.
Correction: Even though her busy schedule, she takes care of her family very carefully.
Mistake: B (buziness) - Should be "busy schedule."

2. My parents told me that I should spend much time to learn English.
Correction: My parents told me that I should spend much time learning English.
Mistake: C (to learn) - Should be "learning."

3. You should take your shoes on when you go into the temples.
Correction: You should take your shoes off when you go into the temples.
Mistake: A (on) - Should be "off."

4. My brother always suggests to read the book before seeing the film.
Correction: My brother always suggests reading the book before seeing the film.
Mistake: B (to read) - Should be "reading."

5. He stopped to smoke because cigarettes are harmful to his health.
Correction: He stopped smoking because cigarettes are harmful to his health.
Mistake: None. The sentence is correct as it is.