Adding new rows and columns works, deleting or merging anything does not. Also cannot change the background colour if selecting multiple cells (have to do them one by one).

It's between Firefox and CKeditor. I tested with Firefox 31 and it worked, and the latest Firefox and it didn't. So it must have broken at some point. Chrome worked.
We don't get involved in the low level bug patching of CKeditor.

It does seem to be this bug, or related to it, although that bug is a lot older than the last couple of Composr versions:
https://dev.ckeditor.com/ticket/10745

I can't reproduce on the latest CKEditor 4 demo, but there are no plans right now to update CKEditor as that is quite a lot of work, and often introduces new issues.

Alright I'll do my table editing in Chrome until it works again :) This seems to be a more current Bug report and is claimed to be fixed @ https://github.com/ckeditor/ckeditor-dev/issues/2003