Ok, so from the .metadata/.log file I can see that there were a few exceptions thrown from SlickEdit when you were starting up the product without a license...then that went away. There is one exception I see lower down where it looks like you had some file open in a non-SlickEdit editor and then did a manual "Switch to SlickEdit", and we failed to open the file. I'm not sure why, but I don't see any more of that in the log so I don't think it was a real big problem.
As far as non-SlickEdit stuff...there are a ton of exceptions logged in there from when it looks like there was a text search going on and for whatever reason some of the files in the project(s) are unreadable. I'm curious, are the files in your workspace local or are they on a network drive?
Now for the worse part...unfortunately I can see from the JVM crash logs that SlickEdit is definitely crashing, probably causing the mysterious crashes you are complaining about since installing the plugin. It is happening in the same exact spot each time, but I've never seen this before...it is likely some artifact of interaction with this particular Eclipse-based IDE. It is crashing when the editor is updating the existing markers in the current file. Can you tell me anything about what kinds of files you are editing with SlickEdit in this IDE, and if possible, what markers you are seeing in the editor? For example, are you setting breakpoints, or bookmarks? Maybe it is just build errors which are populated by the IDE? Any information might help.