When importing fails for me, it usually gets stuck on a certain letter. Identifying that letter has been a key to solving the issue. If some of your key combinations conflict with Keyman’s hotkeys, it will fail.
You can either remove the conflicting key from your code and reimport or deactivate its shortcut for Keyman temporarily. Using a combo that is reserved by default in Kerman isn’t recommended, as others will be unable to use it.
As for Character map, I can offer a partial solution, right click on a letter in the map and choose Insert Mode>Code, Character, or Name. Put your cursor in a code area for typing and double-click on the letter to output any of the three. Dragging doesn’t seem to work in the code.
I mostly work on the code tabs, so I hadn’t noticed that it tended towards character in the GUI as you describe, nor had I tried to drag and drop. Maybe there’s an encoding reason to prefer literal characters in the OSK, but I don’t know.