1. I need to "run" the game twice to start it. First time I double-click the icon, the Windows color scheme changes, but nothing happens. I need to click it again for the game to actually start. After closing the game, the changed scheme remains. I have Win7 Ultimate 64bit.

2. The old cheat codes don't work. Is it a bug or intended?

I'm running it on Win10 and never had issues so I probably cannot help you with number 1.

Which cheat isn't working for you? As far as I can tell all are working on my game.

Turned out they're actually working, except for at least one (I've only checked few of them) - call cousin vinnie.

Also, I checked the task manager, and it turned out that I indeed run the game twice - there are two SC3U.exe processes running. I have no idea why it's like that...

Check the advisors and petitioners window (opened by the 'Meet' button)

That's the problem. It doesn't show up there.

EDIT:
Nvm, it worked finally. Maybe I was trying to use it too early?

I know it works even if you use it before unpausing the first time, so it's not that

Use my guide to get the game running using DxWnd.
DxWnd has a built-in framerate limiter that will mostly fix the main problem. And if you want you can follow the extra steps to make the UI/fonts look bigger on the screen.

https://www.gog.com/forum/simcity_series/fixed_these_problems_using_dxwnd_map_scrolling_speed_high_cpu_usage_small_textui/page1