Super easy is how modern Zelda is made and marketed by Nintendo, so it's no surprise that many Zelda players enjoy that mode of play. But that was not how the original vision of Zelda was. In NES Zelda1 and NES Zelda 2 - The Adventure of Link, there was actually a very different vision of Zelda but that changed after the infamous Super Mario Brothers 2 incident. I'm a traditionalist and I like the old ways of Zelda even though they're mostly forgotten now. I can see that you're mostly into modern Zelda but maybe after you complete IoR on super easy mode, you can just give it a try on hero mode??
No - the NES Zelda game definitely did NOT auto-save. They worked just like you're seeing now. I have the old NES ROMS and emulator you know?
Yes, you have to be careful and tell it to save otherwise you can lose all your progress. That's how the old NES worked and that's how Zelda Classic works too as a consequence.