Is it possible to merge multiple gradients into one object?
For example: a rectangle with two radial gradients in two corners. How can I implement that?
You can add multiple gradient fills to an object via the Appearance panel.
If you need more complex gradients you can use the Mesh Tool to create a gradient mesh. Simply click on a point with the Mesh Tool to create a mesh from the object, you can then change the color of each individual point.
A simply rectangle with each corner point set to a different color:
For more complex gradients just keep adding points:
You can expand an existing gradient fill to a gradient mesh by selecting the object, expanding (Object → Expand) and selecting "Gradient Mesh":