I've had these things happen over time. Almost each & every one of these symptoms. Sometimes combined. Sometimes single. Not so much with VistaHB, Vista E, Win7, or XP Pro (but it has happened), but in particular, when leaving an Ubuntu vm "idle" for several hours. Strange things always seems to happen. Never repeatable. My way to fix? Create a new vm. From my experience with vm's (more than just Parallels) once a virtual starts misbehaving the only thing to do is save what you need (to external) and blow it away.
As a mater of operating, I keep all the data files I need on external - either through "shared files" or through USB connection. (Actually I use both. TimeMachine does a nice job of backing up the shared folders data.) When I create a file in a vm, I *always* "Save As ..." to a shared folder or external drive. At any given moment, I can destroy the vm. Usually I will also can the vhdd, but occasionally I will save it and subsequently add as a 2nd (or 3rd or 4th or ...) data drive. But since I keep my files outside of the vm, this is not usually necessary.
I know this is probably not what you want to hear, but when it comes to a misbehaving vm, just how can it be fixed? Some subtle situation has developed in a particular instance between the guest os, the host os, Parallels virtualization and possibly virtualization support in the chip!. And, where would one start looking for the problem? Parallels? Guest OS? Host OS? (Just because its a Parallels vm doesn't mean the problem is there. I have not found VMWare or VirtualBox to really be any more stable. If you have, then perhaps...) And then what? Would you really expect someone somewhere to look for the problem and develop a patch, when creating a new vm "fixes" the problem.
From what has been said I see multiple symptoms that may not be related to a single problem. One common theme seemed to be with the Mac going to sleep and waking up over time. However, unless you can repeat any problem such that an engineer can also repeat the problem in a test environment so he/she can analyze the interactions between the Parallels software, the guest os, the host os and the chip virtualization support, expecting someone in Parallels to "fix" the software based on the descriptions of the above symptoms is unreasonable. Providing a diary of the events (programs running, what activities were going on) that occurred over time before the symptoms began to manifest themselves would certainly help. But even then, to write specific patch and test it, well...
One thing that has help the stability my VistaHB vm is that I disabled screen saving and created a "Parallels" power options script that has everything either "Disabled" "Never" and "Off". I did see significant improvement in NOT encountering problems like those above. Also I run a background networking program (in the vm) so that there is continuos work going on so nobody goes to sleep (only the Mac screen saver and screen display timeout are set). While not feasible for battery op devices, it did help on my iMac (reference to iMan entries above.) As was noted above, there seemed to be something going on with the mac sleeping and waking up. Remember the host os may also go to sleep and wake up. And somehow Parallels is supposed to coordinate activities between the 2 and their use of the cpu. (I mean I know I've got problems when my wife and kids sleep and wake up at different times
As for the Ubuntu vm, I start it up, use it and then shut it down. I know I don't like this, but leaving Ubuntu idle in Parallels on the iMac is worse. With with vm's, if they start up a work for "a while", there really is no problem to "debug". But when some where down the line, symptoms like what you speak of start up, at that point forget it. Blow it away. Trying to fix it, I've found to be useless. Putting in trouble tickets without logs covering hours and not being able to demonstrate a repeatable problem is not going to accomplish anything either.
BTW, I am not with Parallels, but do have a lot of experience with vm's and debugging software.
As such, my $20 worth.