To apply a gradient fill across multiple objects in Illustrator, select all the objects (drag to select, or shift+click), select the Gradient Tool, and drag out the gradient in the direction you want.
With all the relevant objects selected, click the Gradient tool icon (or press G on your keyboard). Then click and hold the left mouse button to set the start point of the gradient fill, and drag to the end point. The fill will cover all your selected objects seamlessly, instead of filling each individually. Once the gradient angle and distance is set, you can change the colours of all the objects simultaneously by selecting them all at once, or individually as normal.
Alternatively, you can use the eyedropper tool (I) to apply an existing gradient to other objects (pick the objects to change, select the eyedropper tool, then select the gradient-filled object to use as the style for these objects). Then select them all and create the gradient angle as described above.