OS X. Should I quit apps or close windows (red cross button behavior)? I've googled a lot about X button, that doesn't quit app, but simply close the window andnd haven't found a clear answer.  I want to be able to know if  open apps affect battery life or other resources.

Should I quit apps or close windows, letting apps work in background?
One of Mac's most confusing features is the red close button, which you think would shut down an application but often doesn't. When you press X button in the window - you actually close the windows related to the app, but it does not quit. Here's more information from Apple's support pages:

Close windows
When you close an app’s window, the window closes, but the app remains open. If you want to quit an app, click the app’s name in the menu bar, then choose Quit [App]. For more information, see Quit apps.

If you want to quit the app (release the memory, reduce CPU usage, etc) then there are several ways to do this:

Using keyboard shortcut: ⌘ cmd+Q.
Using contextual menu (or application's menu): Go to the Dock at the bottom of the screen and find the icon for the app, then right click (or ctrl+click) to bring up the contextual menu. At the bottom of this list is the Quit option.
Using Activity Monitor: Applications&gt;Utilities&gt;Activity Monitor.
For unresponsive apps: Force Quit (⌘ cmd+⌥ alt+esc)

You may also want to overload the default behaviour, and to make it like in Windows OS, but you need to use separate utilities (like RedQuits). There are a bunch of those utilities that close applications when you click the the red close button.
In overall, to answer your question about how it hits system efficiency, memory and battery: OS X handles it properly and does as much as possible to optimize efficiency, unless the Application itself is written poorly. OS X internally has a lot of optimisations like App Nap which help to keep background apps' effect on system resources to a minimum:

You don’t have to quit apps once you’re done working in them — OS X allows you to work with several apps open at once. Features such as Compressed Memory and App Nap keep your Mac running fast, and save power when many apps are open.