Hey there,
Long-time Warcraft III map-maker just taking a dive into Galaxy. Looks like I've got my work cut out for me. One thing I've noticed (and can't seem to find an answer to on the internet) is that I cannot rename or delete regions, points, start locations, sounds, etc. The options are there, but they're grayed out and I can't select them. I can only delete them using CTRL+Z (that's if I just created them, though). Check out my screenshot. Thanks in advance guys. I'm using Windows 8.1 x64.
I was able to fix this problem by clicking Layer > Select From, and checking-off regions, etc.

I do stuff and thingies... Try widening and reducing the number of small nooks and crannies to correct the problem.
I can recommend using "active layer only" in the selection settings unless you want to copy objects from different layers at once.
But it is really weird that the clear-action is grayed out within the list. I can't seem to recreate it.
Btw, you can use hotkeys instead of using the list:
- 'Enter' for the property window for the selected objects
- 'Delete' to delete the selected objects
Also, 'Space' allows you to switch easily between selection and the placement/creation mode.
Last but not least, you can merge selected regions via 'Numpad 0'.