Q: SPLIT SCREEN - can I like HDMI?

Yes it is possible provided your iMac meets the system requirements (see help section of link).

See the link and note extend your desktop is what you want to do:

Use AirPlay to display video from your Mac on an HDTV - Apple Support

Since it sounds like you already are using the TV as a secondary display with a cable, getting the ATV is not going to gain you anything except a wireless connection.  Since you are using both displays at the same time I am not sure what that gains you.

Unless I am missing something, I would stick with a wired connection.

yes with an appletv you can airplay mirror to the tv so it's like if you connected a second screen to your mac where one is 1 desktop and the other is another