Yup, thats right.
I’m not familiar with this chip so I can’t say with 100% certainty but that is the idea.
Yes, CS GW receives data from nodes and forwards to server.
Yes, although the CS server could be installed on one of your RPIs if you wish, but this is not recommended for multi gateway setups.
Yes, it comes installed on CS OS you just need to configure it to point to your CS server.
I am confused by your setup and not 100% sure I understand your idea. What I gather here is you have LoRa devices that essentially work as a hub for a bunch of sensors. You need to be able to send a downlink from the server to the “hub”, and then the hub checks the sensors (I assume through serial connection or similar and not lora) and reports the sensor data back to CS.
If that is your goal then it is absolutely achievable through CS, although you will have to do some rewriting of your hubs to make them LoRaWAN compatible (this would be considered a class C lorawan device). You can trigger downlinks through the CS UI or API to send data to a device, how that works is CS determines which GW had the best signal strength for the devices last uplink and tells that gateway to send the data (typically hex) on a frequency the device is listening on. How you would specify what hub you want to request data from would no longer be with “srv10” or similar but with the hubs devEUI: a unique identifier each LoRaWAN compatible end device must have.