What is that error message : 1,0,0100,0,0,0

@james I don't see how that is helpful. If you actually looked at most of those links you would notice documentation of the third field of this status response is unclear.

@pierr 0100 is undocumented. I cannot find it anywhere. Here is my post on sparkfun about this:
https://forum.sparkfun.com/viewtopic.php?t=34706&user_select=45522

I even commented on the actual product asking. I've also emailed the manafacturer.

No one knows.

From my experience 0100 means that the PDP context hasn't fully initialized. It is important to ensure you get an OK before you supply it with further commands.

the 0 in your response means socket is not connected. Just look at it and hope for a 1.