Hi I have the original EMS tanks. It's the same device just relabelled.
To answer your questions:
1. Yes you can control it via Wi-Fi on local network, however for initial setup I think you do need Internet connection. The device uses the Smart life app for control. It is a Tuya device.
2. You can add it to Home Assistant through the Tuya Local HACS integration. I contributed to the device recognition, it is called EMS Waterhear in the Tuya Local device listing.
3. This I have not tried, not sure of this can done on Tuya devices. Perhaps someone more knowledgeable than me can answer this.
I have been running on this for almost a year now in HA without any issues. And Magneto/EMS after service has been fantastic.