to your first question. Could it be that the device is two times in the LDMS? We had this for a while that the core server shows up two times in the inventory. Check if you really compare the same devices. Open the inventory of you device that returns in the query and look for the "ID". Compare this ID with the other device where you have the full inventory. Are they the same? If not, you can delete the incomplete one.
To your second question, to bew honest I don't know what you mean...;-) If you can't reach the core, then it seems to me like a Network or DNS issue... The test ou have done only shows you, that the client is listening on port 9595 which means, the services is up and running. But you still need a valid network for the core client communication. Maybe you can define a little bit more in detail, what you problem is here.