For the first one, I skipped the map and went with search + saved cities instead. All your saved places sit on the same 24-hour dial, so you can see the difference from your local time at a glance without doing the timezone math. The upside is that it works completely offline and fits nicely on Apple Watch too.
Your second suggestion is the part I only got halfway right. You can move the dial in 15-minute increments and the daylight/twilight colouring changes with it. There’s also a calendar where you can jump to any date and time and see what the solar state is in every saved city, but right now that’s shown in rows rather than by recolouring the clock itself.
I like your version better though, hovering/scrubbing a time and having the whole clock recolour for that moment would make a lot more sense. I’m going to add that to the list.
I’m the developer, btw: https://apps.apple.com/app/id6797192832