...is a way to download an older Version of Mountain Lion from the App Store?
Nope, your stuck with it breaking things or being buggy, no way to revert to a earlier verison.
If you made a bootable clone you could, simply hold the option key and boot off the clone and reverse clone 10.8.4 back on.
So since you can't go back, you can attempt to fix in place, provided it's not a OS X bug that has to be fixed.
Your likely going to need to do #8 and restore OS X over itself, any third party software that doesn't work, check for a update or problems on the developers forums BEFORE reinstalling it or your problems will most likely return.
What exact version of OS did the machine come with?
If you have a backup, there is one way you could try, but that will wipe out everything on your hard drive: boot into internet recovery (hold Command + Option + R during restart), and once connected to Apple's servers, go to Disk Utility to wipe and format your drive. It will then automatically download/install the original version the machine came with - IF that was lion or Mountain Lion. You can then update if desired.
If it was Snow Leopard or earlier, then you'll need to install disks.
Since Snow Leopard you can.
I've not heard of that; all the suggestions I've seen is that you cannot install Lion over Mountain Lion (as an example) unless you erase the disk first. In fact, I remember I had to do a reinstall while testing last year and had to wipe my disk first to get back to Lion. I do not know about Snow Leopard since I've not used it regularly for 2 years (I have a bootable partition with it and boot into it to use Appleworks occasionally).
And, in order to use Internet Recovery's ability to reinstall the original system, the drive needs to be wiped first. That has been tested.
Thanks for this info
since you can't go back, you can attempt to fix in place, provided it's not a OS X bug that has to be fixed.
Tried everything, Recovery, Resetting NVRAM, checking Harddrive for permission and filesystem errors, performed a Hardware Test, nothing at all. Then i completely reinstalled Mountain Lion, and again, hang at bootup, hang at save boot. It wored all so well under 10.8.4 i really wonder what Apple messed up with the latest update....
Does anyone know if it is possible to import iCal, Adressbook and Mail Data from the Applications in Mountain Lion to the same Apps in Snow Leopard?? I have a Backup, but just the Files in the Library Folder. If i can get these files to work under Snow Leopard i´ll install that one.
If you want to import Mail data, you can try that, but you will need to drill down to the actual emails and import them into newly created folders as the folder hierarchy changed completely. I did this going from Snow Leopard to Mountain Lion and it took hours, but did work when I finally finished. Don't forget to rebuild each mailbox and then restart the computer.
As for addressbook: simply export all of your Vcards (as Export > Vcards) and copy the file from your desktop to the Snow Leopard desktop, then import them from there.
Can't help with iCal as I don't use it.
Have you tried booting into the Safe Mode? I didn't see that in the linked article. Disconnect all peripherals except those needed for the test. Shut down the computer and then power it back up. Immediately after hearing the startup chime, hold down the shift key and continue to hold it until the gray Apple icon and a progress bar appear. The boot up is significantly slower than normal. This will reset some caches, forces a directory check, and disables all startup and login items, among other things. When you reboot normally, the initial reboot may be slower than normal. If the system operates normally, there may be 3rd party applications which are causing a problem. Try deleting/disabling the third party applications after a restart by using the application uninstaller. For each disable/delete, you will need to restart if you don't do them all at once.
I found out that iCal in Snow Leopard will import all Data if you just copy the Files and Folders found in ~/Library/Calendar and ~/Library/Application Support/iCal without making trouble.
For Adressbook: I can´t export data from Adressbook under Mountain Lion as i don´t have access to it, i just have a backup of the files and folders.
Copying Mail Files did work so far, but as you said: It took "ages" :-)
I have been trying Recovery Mode, i tried to boot in Safe Mode with all stuff disconnected, nothing, everything ends up in a Kernel panic. And formatting the HDD and install a "fresh" copy of Mountain Lion (automatically installs 10.8.5) ends up in a kernel panic in Normal as well as in Safe Mode.
To bad that one can no longer download 10.8.3 or 10.8.4 (which both worked just fine for me).
End of the Story: I reinstalled 10.6.8 again, as i am ****** by trying this and that, and i need a working machine.
Regular recovery (Command + R) reinstalls the currently installed OS version on top of what you have.
Internet recovery (Command + Option + R) will reinstall the original OS version - IF that was Lion or Mountain Lion AND you erase the drive first. That would be a "fresh" install.
If yours came with Snow Leopard, internet recovery will not work. You need the install disks.