I was having the same symptoms as #2 with both RC1 and RC2 (though I never saw the error you posted). I narrowed it down to the fact that since the RC, CMS Ajax calls return JSON rather than plain HTML.
Something was causing "\r\n" to be output before the JSON code but after the Content-Length is already calculated, and this meant that the last two characters of the JSON output were truncated (the important "} ) meaning that the eval() fails and the .success callback was never executed.
Over around four hours I narrowed it down to coming from /cms/code/controllers/CMSMain.php, generatePageIconsCss() (of all places), in the $obj = singleton($class) line (around line 412). This loops through all the classes available, and through some trial and error I found that one of my classes in /mysite/code had a blank line before the opening <?php tag.
Note that this wasn't an issue in the beta -- it only showed up in RC -- so you may have one of these stray lines that you didn' t know about. I'd recommend using Firebug to check the result of the CMS's XHRs and see if there's a blank line before the JSON output.
Perhaps Core::singleton() (or one of the methods it uses to get the class) could be tweaked to make it a little more foolproof?