Interpretation of Confidence Intervals using Cox proportional hazards regression model (coxph)

I am using the coxph function to model a Cox regression. By using stepwise BIC selection I obtained an model with 6 variables. One of the variables I had to transform using the logarithm to make it fulfill the proportional hazard criterion. All Variables are marked as high significant with very low p-values- What I am now confused about is the fact, that the confidence intervals of two variables are very high. Therefore I wonder how "useful" those variables are! Since they are selected by the algorithm I have no doubt that they are useful in a mathematical way, but what is the meaning of a variable whose 95% confidence interval is spanning over a wide range.

As you can see the variables log(F) and especially E have a very high confidence interval. How can E be so important for the model (there have been more than 70 variables to choose from) and still be so "uncertainly" determined. I hope I was able to formulate my problem in an understandable way.

Transformations of predictors does not relate directly to the proportional hazards assumption; it relates to the regression shape assumption, i.e., how when varying $X$ the log hazard function changes for fixed time $t$. And it is doubtful that the log transformation is fully adequate, which is why analysts frequently use regression splines.