1. Will the agent be compatible with the new version that will be running?
2. If there is no compatibility, do I need to restart the agent?
3. How much will the downtime be?
Agent installation is typically quite quick
File Server RSCD Agent needs to be at the same version as the Application Server
Managed Server RSCD Agent need to be at the version that provides the required functionality for the platform it is installed on - see the docs links above
Documentation for the Upgrade process is here:
I would encourage you to take advantage of the BMC Assisted MIGration Offering (AMIGO)