The Promo CDr lists it as "Rock Version", so that would be the closest thing to a proper, correct labelling of that version (the CDs had no mention of it being any different from the Confessions version, and the Spotify version had it listed as "I Love New York - Live").
https://www.discogs.com/release/15519652-Madonna-Im-Going-To-Tell-You-A-Secret
Despite this it is commonly known that this rock version is an early version. It was probably mastered for the live album, just like how Back That Up got mastered when its demo got released.
Yes it was. Most of Dallas Austin's work from Bedtime Stories was remixed near the end of the album completion in hopes to give it more of a pop feel, less urban.
Daniel Abraham reworked "Keep On" as "Don't Stop", and "Honesty" was reworked as "Your Honesty". Though as we know only "Don't Stop" made it to the album. "Your Honesty" was then set to appear on the 2003 boxset that got scrapped and the song instead appeared on Remixed and Revisited.
Secret is the only song that appeared on the album with Austin's production intact. Let Down Your Guard and Freedom were later released, but as rare tracks, and Right on Time was left unreleased.