I have the same problem as the op.
Please reread the thread carefully. If you're indeed having the same problem as the OP, you can either use CKEditor or wait for CMSimple_XH 1.5.4, which will be released in about a week (the problem with the inline table background images is already solved in the TRUNK on SF -- but I strongly recommend not to use this version on any production server).
If you're problem is that the styles defined by classes don't show up in the editor, Gert's solution is the way to go.
I am kind of nervous because I don't want to break anything.
Simple solution: make a backup of the files you're going to change -- if anything goes totally wrong, just restore the backups. For small changes you might make use of the clipboard: before changing the file in the back-end, mark the complete content and copy it to the clipboard. Then make the changes and save them. If the modifications don't work as expected, just paste the contents of the clipboard back again.
And well, in the long run we should consider offering an undo facility for editing the configuration, language settings, template, stylesheet etc.