You'll know before you go, and get it fixed. It would have to be a real co-incidence if it stopped working right there. It is not as if it takes days to drive through Death Valley.
I don't think so. The roads are paved, and so long as you stay on them the chances are as great as anywhere else you drive. And even if it were to happen, it is not as if you are days away from help. (That only happens to those who go off the paved roads ill-prepared.) Death Valley has traffic going through it all the time.
Yes you are, but so was I. It took until my third visit to the Southwest, before I was game to visit. All the horror stories I had read, terrified me.
Go ahead and do it, and afterwards, you will have a great chuckle and wonder why you worried. I know, I did.
That place is amazing!
Lifey