I would like to know, in a typical e coli genome what percent of genes the organism could not survive without. That is, if all the other genes evolved except that one, the organism would not be viable.
About 10% in rich media.
There are lots of papers that try to answer this question. The basic way you do it is you knock out one gene at a time, either in parallel experiments or (more common nowadays) in a pooled experiment, and figure out which knockouts survive and which don't.
The most recent study counts 358 essential genes (out of about 4000 genes in E. coli). http://mbio.asm.org/content/9/1/e02096-17.full . Figure 2 compares a few other papers.
The exact answer will depend on the exact conditions you grow the cells in (if you have fewer nutrients or other stressful conditions, more genes will be essential).