Is Texas alimony state, and if I'm filing divorce does my spouse have the right to stay in our home/apartment while divorce is in process??

Texas is not a alimony state.  Texas has spousel maintainece under certain situations; ie been married for more than 10 years; spouse suffering from a disabiliy; married for more than 10 years and spouse lacks the ability to be self sufficient.   In Texas, when a divorce is filed the spouse does not have to leave the marital home.  You might be able to obtain a "kick out" order under certain circumstances.