To elaborate on Adam's reply:
1. you need different ADOMs if you have FGTs with different firmware version as well; Global database is to allow you to create objects you can then push to any ADOM, no matter what firmware it is. You can't really share objects/config between ADOMs, each is its own, isolated container usuallly
-> it depends very much on your FortiManager use case
-> if you're unsure, you can reach out to Fortinet Sales/Professional Services for assistance in assessing what you need and what FortiManager configuration is suitable
2. An ADOM can contain up to the maximum number of devices the FortiManager itself supports. How many devices the FortiManager supports depends on HW model or VM licence. Note that FortiGate VDOMs count as individual devices
3. FortiGates should have an identical configuration in an active-passive (or active-active) cluster, so they will either be in transparent OR in NAT mode (or have VDOMs with both), but if you try to form a cluster with different modes, then the secondary unit will be overwritten