How to upgrade from MAC OS X 10.5 to OS X 10.8 ?
Can I just buy 10.8 as download (can't find in app store now), burn and install ?
OS X 10.8 has not been released at this time. Your ability to upgrade from OS X 10.5 will be based on your own hardware. Apple released all the upgrade information awhile ago I would go read that.
If this answers your question I would appreciate it if you would accept it. You have asked 16 questions and most have correct answers.
Macs that are NOT expected to support OS X Mountain Lion
Macs that will support OS X 10.8 Mountain Lion
Assuming your hardware supports 10.8, and assuming Apple will use a similar distribution mechanism as they did for 10.7, you'll be able to obtain an installer that can be used even to install on a blank disk. For 10.7 it involves downloading the installer and extracting the InstallESD.dmg from inside it (right-click and choose "Show package contents"). You will need to do this from some other computer running at least 10.6.8 with the App Store.
In case a direct upgrade of 10.5 won't be supported by such an installer, you can simply use the Migration Assistant to copy your files and settings. If your system settings aren't crucial for you to save, you can save a lot of time by just deleting the system folders and the installing 10.8 on that disk - your documents folders should remain intact.