Check the door seals. My parents had a similar issue - at least the melting/clumping portion - in their LG FD and on his second visit for the same problem the repair tech ordered a new seal. I was skeptical but it did resolve the issue.

We found the hollow ice cubes to be from a plugged or slightly plugged up water line going into the ice maker. We had a small ice jam near the back now and then. Cleaning out or getting a new water line should be a quick fix. Our refrigerator is a GE side by side...about the same age as yours.

If you have water on the door, how is the flow? We had the same issue as grandma, plugged filter. We were getting small cubes. Replaced 8 year old filter, all is good.

You might go to this site, go to the refrigerator forum and search around. I did a search on hollow ice, and found that link, but it was pretty detailed as to the fix , but a lot was over my head. Here is another post http://forum.appliancepartspros.com/refrigerator-freezer-repair/507547-whirlpool-refrigerator-ed25dqxbw00-ice-maker-not-freezing-properly.html

The suggestions include low water pressure either due to a saddle tap, or clogged water filter, or the temp is too cold,

Here is a link that might be useful: appliance repair forum

Yes, the water in the door is slow coming out also...indicating semi plugged water line/filter in water going into ice maker.