PPCGeeks - Google Sync

Ok, I have questions. I had the answers, but I think they escaped my mind. As far as I know, GSync only allows syncing of your calendar and contacts. Not email.

This sync is push, which means your phone maintains a persistent ActiveSync/Exchange data connection with Google (a little bit of a data hog) -> Myth or fact?
If it doesn't maintain a persistent connection, whenever ActiveSync "connects" to Google it means it simply does the synchronization -> Right or wrong?
If it does maintain a persistent data connection, the push happens almost in minutes. But this is a data hog -> Right or wrong? (If right, how can I make it so it's not a data hog yet useful)
If I already have an ActiveSync source with someone else, forget about adding another one like Google -> Right or wrong? (I use NuevaSync cuz it syncs multiple calendars and it uses the ActiveSync connection)
If I want to add my Google Apps email to this syncing mix, I know the only way right now is doing it as IMAP which literally checks email every few minutes and doesn't have push capabilities -> Right or wrong?
If I do want the Google Apps email push functionality, I know someone of you will suggest apps like Seven. Which if I do go with, brings me to this: Seven runs in the background, (battery/RAM sucker), maintains a persistent data connection (battery sucker) -> How can I minimize/avoid that?

Guys, I understand recommendations might come in my questions but please try to keep it separate from direct answers to my direct questions to avoid confusion for me and future searchers.

Thanks!