Homestead Exemption + Active Duty

1. Do I need to be a Texas Resident to be approved for Homestead Exemption on home purchased in Texas while on Active Duty there?

2a. When I PCS again in the future and decide to keep the home to rent out, am I able keep the homestead exemption on it as long as I don’t apply for a future exemption to another home located elsewhere?

2b. If no, do I need to notify the county tax office that I am moving and intend to rent it and thus lose the homestead exemption?

Thanks!