Are the rules in the game accurately based on Korean?

Yes - you don't have to worry that you're learning incorrect pronunciation or rules.
Just have fun solving the puzzles and learn at your own pace.

How do I reset my data, including the levels and the stickerbook?

On iOS and Android, simply delete and reinstall the app from the app store.

If you downloaded Matcha from the Mac App Store, you'll need to delete the file at/Users/YOUR_USER/Library/Containers/com.delphiniumgames.matcha/Data/Library/Application Support/com.delphiniumgames.matcha/data.json

If you downloaded the Mac app from itch.io you'll need to delete the file at /Users/YOUR_USER/Library/Application Support/com.delphiniumgames.matcha/data.json

On Windows, you'll need to delete the file atC:\YOUR_USER\AppData\LocalLow\Delphinium Games\Matcha\data.json"

For more information, see here.

Is there any way to undo more than once? Or to reset the level without switching back and forth?

Hold down the undo button for 1.5 seconds and the level will reset back to its original state.

Why are some words spelled differently to how I expect, for example "Kim Chi" is romanised as "Gim Chi" in Matcha?

There are a number of different ways that people choose to romanise Korean pronunciation. The Korean consonant "ㄱ" (g) sounds like a combination of the english "g" and "k" when used as the first consonant, so often people will choose to romanise it as "k" instead of "g". We use the "Revised Romanisation of Korean", which is the official system used by South Korea. You can read more about this here.