You can get some real-time data using API method /info. As of now:
"new_active_users": 10,
"total_users": 154488,
"badges_per_minute": 0.17,
"total_badges": 419856,
"total_votes": 2338422,
"total_comments": 1874084,
"answers_per_minute": 0.22,
"questions_per_minute": 0.15,
"total_answers": 532934,
"total_accepted": 198520,
"total_unanswered": 74245,
"total_questions": 363190
The documentation does not state the time interval used for "per minute" computation, but it says that the query should not be invoked more than once per hour, and the number 10 of new users is consistent with this interval being 1 hour. So, it seems that 0.15 questions per minute were asked in the past hour. It's relatively quiet due to a weekend (long weekend in the USA).
For a larger interval of time, see Site List, according to which 609 questions per day were asked on average over the last two weeks. This is 0.42 questions/minute.
Distribution by country
Quantcast offers some data of this kind. It does not differentiate by the kind of activity (posting questions, answers, or just reading). The geographic distribution of visitors over the last 30 days is as follows:
1. USA 45.49%
2. India 9.14%
3. UK 7.17%
4. Canada 6.09%
5. Australia 2.50%
6. Germany 2.18%
7. Philippines 1.32%
8. Pakistan 1.23%
(other countries <1% each)