Your first point is technically correct, but 24-hour days and 7-day weeks are a de facto global standard at this point in history. There are outliers, like the Javanese 5-day week or the experimental 5-day Soviet calendar, but they are few and far between.
I think it was the Babylonians that created the hour/minute/second and a precursor of the meter on the process. It's high-tech bronze-age innovation, that got hyped-out so much that it took the entire Old-World by storm, so the Egyptians got them too.
Is it? I know some cultures have a traditional lunar calendar, but I didn't know there were many that didn't also use the Gregorian calendar for business.
Which cultures have the seven day week without the solar year?
Well, I only know how it tends to work in China, where the traditional calendar is used for cultural events such as festivals, while the Gregorian calendar is used for just about everything else, including domestic business. I assumed it's the same in most modern cultures with a different traditional calendar, but maybe I'm wrong.