Hi
". . . can I install Lion Server on my iMac (Lion OS)?"
Yes. You must install Lion OS before installing Lion Server anyway. As long as the hardware meets Lion/Lion Server's General Requirements you'll be OK:
http://www.apple.com/macosx/server/specs.html
". . . and still use my iMac for normal stuff like (photo-editing, surfing the web etc.)?"
Yes but why would you? If you're going to be running a Server let it do what it's supposed to do.
"Does the Lion Server run in the background?"
Yes. However if you don't configure or enable any services it won't run at all. In which case why install it?
You may find this article of interest?
http://support.apple.com/kb/HT4827
When you purchase and install the Server App and go through the Server Setup Assistant and if you don't enable any of the services presented in the Setup Assistant, at the very least DNS Services (for lack of any further information I've only going to assume NAT) will be configured and enabled. You won't have access to the Service unless you use the command line or download the additional Server Admin Tools:
http://support.apple.com/kb/DL1457
It can't be stressed enough how important a correctly configured and running DNS Service is to the stability of Lion Server regardless of the reason you think you may want it for. Even if all you want to do is use Garage Band, iTunes etc and your aim is to simply 'test' Lion Server, you may find your experience extremely frustrating. Don't confuse running a private DNS Server with what you're familiar with on the Internet.
HTH?
Tony