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What is the assumption we must check if Cox proportional hazard regression is used?

Is my step and method to build on Cox proportional hazard model correct, or not?

  1. Can I used ln(-ln(survival))curve check PH assumption for categorical covariate, Schoenfeld residuals test for continuous covariate
  2. Maximum partial likelihood estimates is used to estimate coefficient
  3. After that use Wald test check significance of coefficients
  4. Stepwise is used to select covariate
  5. Overall goodness of fit of Cox proportional hazard model is check using Cox-Snell residual plot
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