"An independent clause is a group of words containing a subject and verb expressing a complete thought, while a dependent clause is a group of words containing a subject and a verb but not expressing a complete thought."
Therefore, based on these definitions, (bolded words are independent, non-bolded are dependent)
1. "If you don't fix the oven, it will continue to burn". "If you don't fix the oven" is a dependent clause because of the dependent marker word; "if." And, the other part of the sentence is independent because it does not depend on anything, and can be used by itself as a sentence on its own.
2. "While the oven is being fixed, you will need to use the microwave."
Same as the previous problem; the first part of the sentence is dependent because it is marked by the dependent marker word; "While." The other half of the sentence can be used by itself as a sentence.
3. "After the oven is fixed, please make me a lemon pie"
Same as the previous sentences; the first part of the sentence marked with the dependent marker word "After," and the other half of the sentence can be used by itself as a sentence.