Hmm, my response didn't seem to make it so typing this out again.
First off, consider emailing this stuff in instead of posting it. Chances are no one else on these forums will look at the log outputs you are sending and derive anything from them. Plus I check email much more often. This is particularly important this weekend as I'm planning a release tomorrow and only happened to check this thread.
The crash for the syncing rule doesn't seem right. It looks like it happened when adding a new folder, not when trying to connect it to an existing sync file. It could be that the addresses in the trace are incorrect. Can you repeat this on demand? If so, can you email in the sync file you are using?
Unresponsiveness may be due to a crash in the rule status. It's hard to tell from your logs as it's missing info. For future reference, at certain points (startup being one), Hazel will log output that looks like "######<<<something>>> load address: <<<stuff>>>". I'll need those lines to decipher any crashes that get logged later during that run. Those values change each run so they need to be matched up.
When moving a folder, were you adding a folder that already exists in Hazel? If so, that will cause problems. It should be fixed in the patch tomorrow.
For the add rule stuff, same issue regarding needing those load addresses. If you can replicate the bug, please do so, and send me the log lines with the load addresses along with the rest of the log.
As mentioned, I'm doing a release tomorrow so if you want any chance of these being fixed for that release, please email the info ASAP.