I am trying to analysis a dataset with survival data, I am new to cox model and I am not sure how to interpret covariate factors. I have read the survival R package documentation and online examples but I am still very confused.

The covariate I am trying to understand is frailty and contains three levels: frail, pre-frail, non-frail

using:

coxph(Surv(time,status)~ frailty, data=data)
Call:
coxph(formula = Surv(time, status) ~ frailty, data = data)

               coef exp(coef) se(coef)     z     p
frailtynon-frail -1.749     0.174    0.443 -3.95 8e-05
frailtypre-frail -0.415     0.661    0.275 -1.51  0.13

Likelihood ratio test=21  on 2 df, p=2.78e-05
n= 151, number of events= 70 

First it doesn't give me a line for the level frail, is there a way to get it ?

Second the exp(coef) and p-value of the level non-frail are low does it means that going from non-frail to any of the two other levels (frail,pre-frail) as a significant decrease on survival.

Third the p-value for the level pre-frail is not significant, if it is computed using frail and non-frail, is there a way to compute it without using non-frail?