I assume you mean Midea, not Media.
No, that’s not how HA works. Check the available integrations - there is only one for Midea, but only for CCM15 devices. I don’t know what that means, or whether it’s compatible with your device.
For the integration I mentioned above, it should still work because the integration uses Local Polling.
Yes it can via automations, but I think there’s more suitable options which might be more suitable for you, like the generic thermostat (though that doesn’t seem to have a fan mode, which the climate integration has)
You might also be able to use this and get rid of the app entirely. You can check if your device is supported here.
Note that I do not use any of the above. All my replies were based on searching the forums and the HA docs. Should you have any more questions, I might not be able to answer them, but others might.