1) Prospero raises a tempest in order for his brother's ship to shipwreck on his enchanted island. [Grammatically correct]
2) Actually, he was deposed by his brother because he loved magic more than the affairs of state. [Grammatically correct]
3) The Duke of Milan and Ferdinand are traveling on the ship. [Grammatically correct]
4) Ferdinand thinks his son had died, although he wanders through the island. [Grammatically correct]
5) Desdemona confesses to the court that she had freely gone with Othello and married him for love. [Grammatically correct]
6) He tells him that they are having an affair. To prove it, he tells him that he used to wipe his brow with Desdemona's handkerchief. [Grammatically correct]
7) Remember to use the simple present tense when summarizing the main events in a plot. [Grammatically correct]
8) Hamlet wonders at the first player's skill in conveying sorrow. [Grammatically correct]
9) He fears what Caesar would become if he were to turn into an absolute monarch. [Grammatically correct]
As for a good site to find the meaning of sentence connectors and exercises on their use in a context, you can try using "Grammarly" or "EnglishGrammar.org." These websites provide comprehensive explanations and exercises related to grammar rules, including sentence connectors. Additionally, you can also refer to reputable grammar books such as "The Elements of Style" by Strunk and White or "A Practical English Grammar" by A.J. Thomson and A.V. Martinet. These resources will help deepen your understanding of sentence connectors and their proper usage.