2. A standard nonzero TTL is otherwise not very meaningful as long as subscription is active. Section 6.3.1 explains the TTL field of a PUSH message clearly: https://www.rfc-editor.org/rfc/rfc8765.html#section-6.3.1
But this mechanism does not replace normal DNS, only supplements it, so no, you probably still need to set TTL.
TTLs could be kept quite long, though, since they'd only be used when push updates are not occurring.
Take a look at: https://www.rfc-editor.org/rfc/rfc8765.html#name-push-messag...
That section contains most of the RRset remove notifications.
Push notifications occur when the primary is HUP'd or restarted, telling the secondaries to pull fresh zones so that everybody's is known to have the same serial. After this the secondaries poll the primary every 'refesh' seconds to check for a newer copy of the zone.