How do I replicate these two effects in Photoshop?

Question 1

I am having trouble finding help on my own since I do not know the names of these effects. Here’s the reference image:

iamges

How do I replicate the impressed circle effect behind the button? I
tried playing with the inner shadow blending option with a
radial gradient, but I failed to match the spherical depth shown in the image. I also tried using the bevel and emboss option,
and while the produced effect is more accurate, I cannot duplicate
the sharpness of the circle’s edges, as well as the subtle highlight
at its bottom. (I do not know how to add blending options to an
emboss).
How do I reproduce the shape of the actual button in Photoshop? I’ve found tutorials on orb-like buttons and flat, raised ones, but the button in the image has a depth and shape that is a combination of the two. (Similar to a flat pebble).

If someone could lead to terms for these effects, that would be really helpful as well.

Question 2

I created a double gradient effect and added a very faint outerglow for the inner circle to give it some texture.

enter image description here

Answer