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Good news, the Dongle-E and ZHA are not bad choices at all as mechanisms to control your zigbee devices, and is the currently recommended method for new starters, but there are other ways.
Lets start with pairing and Aqara devices.
Sometimes, these devices don’t fully pair before they go back to sleep. To stop this, you usually short press the button that you long pressed to start the pairing process. This keeps them alive. I’d try this with your cube and see if you can get it paired.
Once paired, that means the device is simply connected to the zigbee network, it doesn’t necessarily mean that it will operate correctly.
Some devices require custom code to be written for them to work, because the manfacturer has decided not to follow the zigbee standards.
For ZHA that requires a custom ‘quirk’ if its not already been adapted into the version of HA that you are running.
For instructions on how to setup custom quirks, take a look here as an example:
I use 5 quirks for a variety of devices (some Aqara) to get them to operate correctly.
I’m surprised however that the door sensors aren’t working straight away. I’d be tempted to restarted HA again just once more, as very occasionally devices don’t seem to fully work immediately after pairing.