I am applying for Executor of my Mother's Estate. The home She left us has a reverse mortgage. Can I evict him and sell ?

You need to furnish a three-day written notice to evict by following the procedures of TPC 24.005: http://www.statutes.legis.state.tx.us/Docs/PR/htm/PR.24.htm. Then, if he doesn't vacate, you'll need to file an eviction lawsuit in local JP Court in Tarrant County.

If the he is your mother's husband he has a lifetime homestead right subject to the rules of abandonment. Until you are appointed executor by a court you have no power to deal with your mother's property. To be an executor, there must be a will. If no will, you can be appointed administrator, but if your mother was married, her husband has a higher priority. You need to hire a probate attorney ASAP.

Who is "he"? The answer to this question is an important fact that is missing. If "he" was the husband of your mother, then he has the right to live in the house for his lifetime (called a "life estate", but he also must maintain the house by paying expenses. Your inquiry suggests that you have submitted the will to probate or some other type of administration of her estate. Contact a probate attorney right away to determine the next step.