Make outbound call

AgentDialer Ver 7.2.3, Enterprise 4-line: Is it possible for the remote agent to make calls without anyone actively making calls from the server?

Yes, but that is for a different product. What you need is Flex PBX, which will allow remote agent to make an outbound call, just like making an outbound call from an office extension.

Also, I loaded the current version, release 7.4.3, on the remote PC. Is this compatible with version loaded on the service (7.2.3)?

No. You should make the gateway server version the same as the remote client version.