Photoshop: Is it possible to combine/merge two shapes created on two different layers?

You can open a closed shape using the Direct Selection tool (white arrow). First, make sure there aren't any selected anchor points on the path. With the Direct Selection tool, click on the segment of the path you want to remove and press Delete/Backspace. This will delete the selected segment, leaving an open path.

Let me know if you run into any problems with this.

Thank You so much, Jeanne... helped a lot..
One more thing, can we give a gradient (from the tools bar) to a shape..???

You're welcome!

You can't draw with the Gradient tool directly on a shape layer, but you can add a vector mask to a Gradient fill layer.

Here are the basic steps:
1. Go to Layer > New Fill Layer > Gradient.
2. Name the new layer and click OK in the dialog that follows.
3. In the next dialog, choose the gradient and its settings. Click OK.
4. Select a Shape tool and set it to Path mode in the options bar.
5. Draw the shape as a path on the image.
6. With the path still visible, go to Layer > Vector Mask > Current Path.

In the Layers panel you should now have a Gradient fill layer that you can double-click to edit. You can also edit the vector mask just like on a regular shape layer.