You can't add 'physical' depth to a 2D, which is a plane surface. It's theoretically impossible.
The image depth illusion would come from sprites you use. If you look at first image you can understand that there are 2 levels of mountain, but without shadows it kinda looks like they share the same surface. Get what I mean?
And if you want to make so your character can 'climb' mountains or slopes, the way to achieve this is to manage your collisions properly. For example add collision shapes to your ground tile walls, leaving the grass or rocks part empty, so your char will bump into walls, and walk freely on the floor.