Generally, Smart Launcher does not drain your battery faster than your built-in launcher, and depending on how you use it, it may also improve your battery drain.
Smart Launcher has been designed and is continuously optimized to use as few resources as possible and when it is running replaces the built-in launcher. Extremely few tasks are performed while Smart Launcher is running in the background (SL reacts to app installs and uninstalls by creating or deleting some icons).
However, even if Smart Launcher might consume less battery than your built-in launcher, your battery usage is much more influenced by other factors, like how and how much you use your device but also conditions that do not depend on you, like network quality and environmental brightness.
Finally, the Android battery stats are not always reliable. If you start noticing something strange about the battery usage of Smart Launcher or any other app, we suggest checking your battery stats regularly to see if the problem persists.
Yes, Smart Launcher adapts to the refresh rate allowed by the system. If your phone supports 120hz and the OS allows it, Smart Launcher will run at 120hz.
No, by no means.