Yes, some companies offer remote computer support 24 hours a day. These companies provide services such as virus removal, software installation and upgrades, and routine computer file maintenance.
There are areas on Earth that can receive 24 hours of day and 24 hours of night - but not at the same time. North of 66 1/2 degrees latitude N. (the Arctic Circle) will receive 24 hours of sunlight...
24 is divisible by 2, 3, 4, 6, 8 and 12 so that it is easy to define half a day, a sixth of a day etc. 13 is a prime so even half a day would require working out half an hour.
The 24 hour day and 60 minute hour originated with the Babylonians, who based their calendar on the earlier Sumerian and, perhaps, Egyptian calendars. The Encyclopedia Britannica has a number of good...