How to "lockdown" a phone for users.

Hi, I'm new to XDA. I'm an android developer, but this is a bit outside my wheelhouse. My company is providing no-cost phones to low-income disadvantaged families for health care and health monitoring purposes in conjunction with a local hospital and local health departments. We developed the app in conjunction with local health departments, and we are procuring the devices ( LG G2 (VS980) ) from a wholeseller of refurb phones. We would like to "lock down" the device to prevent abuse and eliminate company liability. The devices remain company property and will (hopefully) be recovered and re-used for other patients when a patient leaves the program. These devices are solely for the purposes of the program and general purpose smartphone functions are only permitted when not affecting the data/voice/sms service plan. (i.e. Calculator)

While I am capable of using Google, I keep finding information about parental locks. I am looking for information specific to:
1. Restricted dialing to a few numbers that we specify (We might have to provide a custom dialer, 911 service ok)
2. In-bound only SMS, No outbound SMS AT ALL (We might have to provide a one-way only SMS app, replacing the default - How to remove the default app?)
3. No ability to install other apps, no google play
4. Auto-update of our app with no google play account needed
5. Restricted web browsing to servers we list (i.e. only patient web portal)

Many thanks in advance.

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