IMac 10.6.8 Build 10K549: Reinstalling OS or use as external monitor

I have an iMac 10.6.8 and I would like to reformat the harddrive and reinstall OS without the installation disk. I would like to do this, and use it as an external monitor so I have 2 issues.
1. I only have 1 GB of RAM, so I cannot upgrade to Mountain Lion 10.8. But if I could, can I open OS X Utilities by restarting the computer and holding option or Command & R. I'm not sure if this is possible.
2. To use it as an secondary monitor: Can I use Air Display after purchasing the client app on my iMac? I'm not sure if this can be done on devices besides iPads, iPhones, etc. Or is my best option to buy a mini display port to HDMI adaptor, HDMI cable, and a HDMI to thunderbolt adaptor?
Any advice or input would be greatly appreciate. Thank you in advance for your time!
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1, You can reinstall without a disk if you first clone your entire system to an external drive using CarbonCopyCloner or SuperDuper - you can then boot from the external and erase your internal and clone it back.
Command + R will not work on 10.6.8. That was introduced in Lion, but it only works with certain older machines because the needed firmware is only compatible with certain models.
EFI and SMC firmware updates for Intel-based Macs
You would also need to add RAM - 2 GB really is not enough, it will result in a sluggish performance; Lion and later should have a minimum of 4 GB.
2. Can't help with that except to say that an older machine will most likely not support Air Display.