1 ..... she looked out of the window, the sun was shining.

Step 1: Analyze the sentence structure. The sentence describes two simultaneous actions: looking out the window and the sun shining.
Step 2: Choose the conjunction that indicates simultaneous actions. 'While' is used to connect two actions happening at the same time.
Step 3: Select the correct option. Option A, 'While', fits the context.
Answer: While