There are two main difficulties you will face in writing these two reviews. The first is deciding whether, in fact, your teacher does want reviews or just summaries or book reports.
A review is normally evaluative, written by a critic to help people decide whether they want to invest money in tickets for a play. Usually a review is focused mostly on evaluation -- whether the playwright and cast did a good job -- and does only a cursory amount of summary. A typical student book report or summary, which seems to be what is outlined above, is more neutral and factual, simply describing the main elements of the play.
The other difficulty you will face in writing this is the very limited word count, which will make it difficult to cover all of the required points. You probably want to avoid choosing King Lear because its prominent subplot would make it difficult to cover in the allotted space. Much Ado About Nothing poses similar difficulties in that the Beatrice and Benedick subplot is at least as interesting as the narrative concerning the main pair of lovers. For Hamlet and The Tempest, you can focus more narrowly on the main arc of the story.
In the case of The Tempest, you could focus primarily on Prospero, and the play as his effort to avenge his usurpation and reclaim his dukedom. In the case of Hamlet, there is a clear, unified plot line having to do with Hamlet's revenge for his father's death at the hands of Claudius.