So let's go down the list...
1) You can if its Windows 8/10 via the OMA-URI protocol, but why would you? The ConfigMgr agent will give a way more detailed overview of the system than the Intune MDM one. For Windows 7, this is true - it's either the Intune agent or ConfigMgr agent
2) Yes - once you link Intune with ConfigMgr, all data and monitoring is shunted into the ConfigMgr console. There's a caveat here, and that's with devices that have the actual Intune agent installed. These will NOT show in the ConfigMgr console, only on the web portal. I've already raised this issue with Microsoft, we'll see if they ever do anything about it.
3) Partly. It is true that once you hook Intune into ConfigMgr, you create all the policies and configuration items in the console, which will then send them to devices via Intune. As for seeing your Windows device in the portal, it depends on how you're linking it - whether by ConfigMgr agent, Intune agent, or OMA-URI protocol.
4) When you link Intune with ConfigMgr, think of Intune as a secondary site in the cloud. It gathers data and hosts a database, but basically all the management is done by the primary site (aka your on-prem ConfigMgr infrastructure). So all configuration and policy management is done through the console, and ConfigMgr will automatically take care of managing clients, whether mobile or full clients.
Hope that helps a bit!