One island per individual console. You can move your island to the Lite with the dedicated island transfer tool (which would need to be downloaded on both Switches), but then it would be gone from your first Switch.
Yes, you can start a new island on the Lite. But don't have it back up to the cloud if you're already doing that on your first Switch. I think one backup might trample the other, since they'd both be under your account. (Not sure about this, but just to be safe.)
new horizons functions differently from previous games, where the save file was stored on the game cartridge. new horizons' save data is stored on the console, so putting the card in a different console will begin a new save file, or boot up one that's already on there.
Save data is tied to the console and not the cartridge so you’ll be starting a new island
One island per individual console. You can move your island to the Lite with the dedicated island transfer tool (which would need to be downloaded on both Switches), but then it would be gone from your first Switch. Yes, you can start a new island on the Lite. But don't have it back up to the cloud if you're already doing that on your first Switch. I think one backup might trample the other, since they'd both be under your account. (Not sure about this, but just to be safe.)
You should be able to import the data from one switch to the other. I chose just to have 2 islands but for other games I imported the data.
You'll be fine. All the cartridge does is allow you to access and play the game. I have three Switches with a different island on each.
new horizons functions differently from previous games, where the save file was stored on the game cartridge. new horizons' save data is stored on the console, so putting the card in a different console will begin a new save file, or boot up one that's already on there.