No, the BLE identities of these tags are currently practically indistinguishable from original tags, and could be made completely identical if necessary. In fact, changing the device's MAC address is part of the specification. What they could block, is the method used by these projects to fetch encrypted location reports. However, the original OpenHaystack project (this one) needs to run on macOS and lets the system handle account authentication, so it's unlikely to get blocked any time soon.
Yes, because they get a commission for every device registered on the network.
In the join process, there is a key that is shared only for developers who paid the fee - which is why it's not really trivial to create an AirTag clone without dumping the Apple AirTag flash