Does that include for example Facebook notifications? So if push is off it will use the fetch schedule I set?
Are you talking about in Settings-->Mail, Contacts, Calendars?
If so, that is strictly a setting for Mail. It has nothing to do with Facebook.
We'll it does say "New Data will be pushed...."
https://macrumors.zendesk.com/hc/en-usHello?
Bumps. Posts that bring a thread to the top of the New Posts list but add no content to the thread (bumps) are not permitted. This applies not only to posts that say "bump" but to those with the intent to bump, e.g. posts saying "anyone?" or the equivalent. See why and how to avoid bumping.
Apps are push or manual for data transfer
If you have push mail / iCloud it utilises the same open connection to push app data as apple control it. Theoretically having multiple apps push won't be a major battery drain. Exception to this is if you have frequent push notifications throughout the day from apps like Facebook or Twitter. If they keep turning the screen on every 10 mins and pulling in data it's going to drain battery quicker.
So I should keep push on? I don't have a email setup but I do have Facebook, Twitter