Samsung Galaxy S3: Memory problems

I'm not sure yet on what is the cause or what will be the solution but I came to a headeach on a problem I'm having with my Samsung Galaxy S 3. The problem is this one, although I have plenty of memory on the device I can not install more applications because it tells me that there is no storage space available.

I'll paste a few screenshots of both the computer and the device itself and I will make a public plea for help because I've been looking at forums, mainly in English, and have not found a possible solution. I think, is an assumption, that the problem is in how Ice Cream Sandwich handles device's internal memory. As you know, the SGS3 brings more than considerable internal memory, with 0.98 MB RAM and 11.2 GB of internal storage it should be more than enought and should have no problem unless the system bad manages memory itself. I think, I say, I BELIEVE, that Android ICS is screwing and is the  ultimately responsible for the mismanagement and let me explain why with a few screenshots:

This first screenshot is Airdroid interface (recommended program to manage your phone from your PC and move images, videos, and contacts in both directions. I have marked in red something that shocks me, it has detected as internal memory and a as SD card the same amount of data. See? so, Link2SD has the same wrong detection:

Link2SD did not detect the second storage card (just format it, just has not caught by this because the system if the catches). In Settings / Storage see this:

It's where I wanted to go, the system recognices the SD card but for whatever reason the other applications use or recognize the internal memory as external storage and do not recognize the real external storage. I would say, without the possibility or the time required to debug the system, that something is going wrong in the management of external storage and communication between the system and applications .

What do I do now? Do I have to uninstall some application before installing other applications? Any recommendations? I deleted caches, I deleted the folder Android/data, I have stopped applications and services and I still get the message that there is not enough storage space every time I try to install a new app.

I will continue looking for answers and solutions and when found I will update this post.

Thank you.