Is Apple’s native iOS mobile device management built inside the iOS
itself?
Yes , Apple has secured mdm-client bundled in each Apple product . We can make use of the client upon enrolling . There is supervised enrollment where mdm-client can perform more privileged task .
Can MDM server manage device (install apps, disable camera, iTunes...)
without installing a MDM agent app?
Yes , Once device is enrolled you can apply restrictions on iOS and macOS , install apps silently using VPP etc . Refer Configuration-Profile-Reference.pdf Page 67 for list of all restrictions
How can the device itself can communicate with MDM server and install
profiles sent from server automatically?
Like iOS apps , mdm-client responds to notifications through APNS . The server in which device is enrolled will have push-magic string,device token and a topic device listens to these helps the server to notify device . Device will then ping the server. I have attached Official MDM guide that you can refer for more details.
Do I need an enterprise account to use iOS MDM service?
Here you have two options , if you want to build your own MDM solution then like i said before you would need to notify device so that it contacts your MDM server upon enrollment . Similar to building iOS app , you need an developer account to create a APNS certificate (refer here) to notify default mdm-client.
Or you you just wish to manage your device , you need not require a developer certificate. MDM vendors would use their certificate for signing, and you would need an apple id account to use upload certificate provided by your MDM to notify devices.
Where can I find documents about MDM API and how to use it?
Refer below links to getting started with MDM . Comment your queries for any help.
1. Setting up MDM and MDM Protocol
2. Restrictions and other MDM profiles
3. Apple business manager