Can you control an iPhone remotely using Mobile Device Management protocol? or any other protocol/service? Of course, the user's consent will be obtained before performing any actions. I am mainly interested in changing the settings and manually selecting a carrier on behalf of the user. Any suggestions are welcomed.
Settings have many MDM hooks. You can experiment for free cloud based solution like JAMF now to get started.
Carrier settings are much more tricky, most get set by the carrier over the air and depend on whatever sim is sent out and physically installed, so you’ll likely need something other than a MDM for that.
If you have setup the iPhone already using the Apple Configurator 2 you can remotely change settings or remotely wipe the device. The idea being you have control of the device because you own it, therefore you are able to control the device from anywhere. Otherwise apple devices don't really allow remote control.
See this article for more information on how to remotely configure a device here.
Unfortunately you cannot remotely control an iOS device. However, many things can be configured, including SOME Carrier Settings (namely APN settings for data - not selecting specific carriers), using a Mobile Device Management product (options include MobileIron, XenMobile, AirWatch, Apple Profile Manager, Lightspeed, JAMF, etc). If you are using a device configured with Apple School Manager and Classroom you can also view the screens.
Some settings can only be configured if you have supervised the device, which can be done either with Apple Configurator, or with the Device Enrollment Program.