No, at least it’s not recommended. Documentation said that it should be external machine. This is because many reasons,. First it is optional component. You don’t need it always (it’s not the same as collector in Appmon).
If you want to have one you can use it for:
No this is not possible. Installer will refuse to install the ActiveGate if cluster node is installed on the host.
Actually, there is an ActiveGate running on each cluster node, but you don't have much control over it (you cannot use it for memory dumps).
Can I use it for Synthetic Monitoring? I am not seeing such an option there.
No you need external one.