That is called code. Ever heard of an emulator.
Cells can metabolize for some time without DNA.
Sure, those are called chemical reactions. A computer can save some data as the power crashes.
And mutations are not typically fatal. That is due to the fact that the cell repairs all but a few percent. Ever seen the blue screen of death on a PC? That is due to the fact that the system is ensuring a "mutation" in the code is fatal whereas, it could just reload and restart.
Repaired mutations are not really considered mutations in a discussion of evolution.
Mutations that affect the germ line are generally not fatal because most of them occur in non-coding regions, or produce synonyms.
Fatal mutations in single celled organisms are not threatening to the population for the simple reason that the population can generally reproduce faster than the available food supply anyway.
In sexually reproducing organisms, fatal mutations are expressed as defective sperm or eggs, and are easily ignored, for the same reason as with single celled organisms. Every living thing is at one time or another in its life cycle, single celled. And the single celled stage includes far more individuals than will survive to reproduce.
But let me ask a question: are you saying that a cell with its DNA removed is "just chemistry"?