a) The movie's plot was 30 years ahead of its time. As Britain commences a series of secret flying tests of its new aircraft, a foreign power seeks to foil their efforts by using a a disguised ship armed with a primitive EMP to bring down the aircraft. To cover their tracks, they have disguised the ship as a salvage vessel, which allows them to salvage the wreckage and kidnap the crews, leaving no clues for the authorities.
If this plot sounds vaguely familiar it's because you've seen it at least four times since. With modifications, this is the basic template for You Only Live Twice, The Spy Who Loved Me, Moonraker, and Tomorrow Never Dies. By extension, not only is Q Planes the inspiration for the most iconic image of James Bond -- as a gadget-happy superman foiling schemes of world domination -- but Austin Powers, Archer, The Incredibles, Kingsman: The Secret Service and all the other films and TV shows which have used that icon as a template for parody and homage.
b) This one is fairly obvious. In the role of secret agent Major Hammond, Ralph Richardson is the polar opposite of what you would expect -- an eccentric English gent with a bowler hat and an umbrella. Preferring brains over brawn, and trading romance for the job (there's a running gag involving Hammond's eternally postponed date), it is easy to see the influence of Hammond on the character of John Steed (Patrick Macnee) in the seminal British TV series The Avengers.
|I see you Macnee...|
Why is this important? Well, Thunderball introduced Bond's most famous and enduring foe, Ernst Stavro Blofeld and his organisation SPECTRE. Blofeld and SPECTRE would be the antagonists in all of Bond's cinematic adventures (except Goldfinger) between 1962 and 1971, and provided the inspiration for other films in the franchise. Thunderball's publication unleashed a 50 year legal battle as McClory and Whittingham fought for credit of Blofeld, SPECTRE and the basic story. These legal complications would lead to a rival production in 1983, Never Say Never Again, and more significantly, put an end to the presence of Blofeld and SPECTRE in the official Eon franchise. It would not be until 2013 that the rights to Blofeld and SPECTRE would be re-secured by Eon.
If you are curious, you can check out the film here.