Adam was genetically perfect. It was not until after the fall that genetic mutations would begin. This is why, to begin with, there was no great genetic problem in a brother and sister marrying. This, as an aside, would answer the age-old hoary chestnut about who Cain's wife was. Adam was also biologically immortal.
Biological immortality is a possibility even today.
The mother could divide again. Unless something deliberately kills the mother, however, there is no reason for it to die. It is biologically immortal. Biological immortality does not imply that something will never die. It simply implies that it will not die unless killed.