1. We were weeding the vegetable bed and picking ripe tomatoes is the correct sentencing of the fragment.
2. It would be the third one "my brother was careful to avoid driving during rush hour" because this is a sentence and in the first choice makes the fragment turn into two fragments.
3. Add "turn" to the beginning of the fragment. This makes the fragment into a sentence.
The correct answer should be locate basic information.
When you are doing the preliminary research, you are just reading through a bunch of sources and information that you may or may not use while writing. You still aren't deciding which exact sources you are actually going to use, but rather just trying to find them and later on make that decision during another stage of writing.