The hormone replacement will help stabilize her cortisol levels. She will need to take cortisol for the rest of her life. Keep in mind that the CBC blood tests will show slightly elevated levels of white blood cells. That is normal in people who take cortisone.
Yes, it seems like she can have a normal life.
https://www.cedars-sinai.org/health-library/diseases-and-conditions/e/empty-sella-syndrome.html - it is not life-threatening.
She may need to be monitored occasionally, but that seems to be it. It's awesome that you care so much for your mom, but know that millions of people take these meds (levothyroxine is also used to treat thyroid disorders), and are just fine. :)