Tablet shows "Low on memory" warning even though internal memory is greatly empty
The internal memory is split into partitions, one of them is /system, which I believe is the one with 13.65 GB in size, this one is mounted read-only, meaning you can't install apps on it.

Another partition is /data (the 0.98 GB maybe, i'm not sure though), it is mounted read-write, and it's where apps are installed.

I think there is an option to install apps directly into external storage (your SD card) or at least relocate them from /data partition into SD card.

Yet another option, is to root your device and allocate more space to /data partition.