You could try with other constants from the literature or calibrate it using a single element model (a cube) and test data. Maybe use a simpler Neo-Hookean model first. It can be based on linear elastic constants. See this thread on the CalculiX forum: Hyperelastic Pipe - CalculiX (official versions are on www.calculix.de, the official GitHub repository is at https://github.com/Dhondtguido/CalculiX).
Yes, you can try with more steps. Just define BCs (and their propagation) following these rules: Understanding multistep analyses