Can xposed framework impact system performance and battery? I've installed Xposed framework and Sense 5 Toolbox module on my HTC One X and doubt that if it is draining my battery and causing the system to slow. 

I've checked with Watchdog and Setting-Apps-Running but seems like there is no background service running. What I thought was there must be service monitoring the user actions but it wasn't.

I would be very appreciate if somebody answer the question from title and explain how xposed actually work on Android.
Xposed isn't a separate service: instead, it's a wrapper in every process, which replaces some built-in functions from the Android framework.

For this reason, it's very likely that it'll have some effect on system performance, but exactly what effect depends on the particular modules. For example, it would be possible (but unlikely) for a module to replace a built-in function that's called frequently with a different version that runs more slowly and uses more battery (and probably even gives the wrong answer at the end).