Is the MAC address pool from which Bluetooth, Wi-Fi, GSM cards etc take their addresses from the same address pool as the ethernet MAC address pool?
Yes. These are 48-bit addresses and the IEEE manages the assignment of addresses from this space.
In my opinion it should not be the same pool because it would be no problem if a Bluetooth Device and a Network Interface Card in a Personal Computer have the same MAC address? It is not possible, in my opinion, to have a collision.
Your opinion is simply wrong. There is no reason someone cannot run IP over Bluetooth and bridge the Bluetooth connection to an Ethernet LAN in a similar fashion that 802.11 traffic functions.
Even if a Bluetooth device would somehow be connected to an Ethernet LAN it would be through some sort of network adapter and the network adapter should have a MAC address of its own and that MAC address will be the one that will be used to communicate in the respective LAN. Is this right?
No, this isn't right. As I stated above, one could create a "Bluetooth access point" and bridge the traffic to the Ethernet segment. It would not require any sort of network adapter with an independent MAC address.
Just because it hasn't been done (to my knowledge) due to a number of reasons that make this impractical, doesn't mean it isn't possible. Edit: not overly familiar with Bluetooth, but a quick follow up web search for "bluetooth to ethernet bridge" turns up a number of such devices. So there may be devices out there already doing this.