A few related questions with regards to game shows:

a) QUESTIONS: 
Do game shows share a databank of questions or do they design it
themselves? If the former is true, how does one go about purchasing
such a databank.

b) GAME SHOW RIGHTS
What sort of rights are owned by the "Who wants to be a millionaire"?
Is it just trademark on the name or do they have a patent on any quiz
game that doubles the stakes with each question? Are the rights
limited to TV? If one invented a quiz game with another name, slightly
different rules and a non-tv application - would it be breaching
anything?

c) OTHER GAMING APPLICATIONS
Can you provide links to non-tv gaming applications, such as internet,
mobile phones, etc. How is revenue raised in each application?

I can respond to (b).  "Who Wants to be a Millionaire" is a federally
registered trademark (registration number 2650948) in the United
States, currently owned by CELADOR INTERNATIONAL LIMITED, 39 LONG
ACRE, LONDON WC2E 9LG, UNITED KINGDOM.  It is likely they own certain
international trademark registrations as well.  Thus, it would be
problematic for you to use a confusingly similar name for a game show
in any jurisdiction in which Celador has rights.  Remember that rights
in trademarks accrue through use, not through registration.  Thus, any
jurisdiction in which someone was using "Who Wants to be a
Millionaire" as a mark for entertainment services would likely have
better rights over your use of any confusingly similar mark in a
related line of services.  As you infer, however, this does not stop
you from using a non-confusingly similar name on a game show that has
elements similar to "Who Wants to be a Millionaire," as long as you
did not infringe the owner's copyrights or patents.  I did a quick US
patent search and could find nothing suggesting they have a patent on
this style of game play ("quiz game that doubles the stakes with each
question").  So, as long as you don't infringe the copyrightable
elements of the game show, you should be OK.

The UK game show 'Double Your Money', ran all through the 1960's and
early 1970's. At that time questions started at £1 and went to £32.
Between £64 and the top prize of £1000 contestants had to go into a
soundproof booth  and listen to the game show host over headphones. I
doubt that 'Who Wants To Be A Millionaire' can claim originality for
the concept but I believe they have some rights over the present
format including: studio layout; lighting; background (heartbeat) type
music as well as ask the audience; telephone a friend and 50/50. I'm
not a legal person so I don't know for sure what these rights might
entail.

Regarding the authorship of the questions, there is no common
"databank." Each show has its own staff of writers. I used to know a
fellow who had been a writer for "Jeopardy!" (This would be my dream
job, if I didn't already have my dream job here at GA.)

Thanks guys (and gals) for the collaborative effort. 

It would seem that:
a) There is no such databank. (Can anyone think outside the box of a
way of acquiring a large collection of quiz style questions?!)
b) So long as you don't infringe trademark, or pass-off as being
related to "Who Wants etc." - a variation should be fine
c) Any ideas for other gaming application?