*Why fuel-injected engines, what would happen if your primer kept operating while climbing with a SEP, temp range carb icing?
Reduced susceptibility to carb icing and the effects of g, better and more even fuel distribution, smaller parts count. A stuck primer may flood the engine. Between 0 and 15 degrees Celcius OAT is the worst range, but some charts show the possibility of icing occurring between -15 to +35.
*What is the maximum operating ceiling of a typical jet?
Late 30's, early 40's due: Fuselage strength/weight (due pressurisation), lack of power to poke to there and once you are there, insufficient stall and buffet margins. However, once you get there, flying can be easier because there are not so many aircraft up there, thus better routings can made.
*Why will a jet not fly this altitude?
See above. Or if it can get there sometimes, but not today it could be due to current weight or SAT limitations (for poor Embraer drivers).
*When will a jet be able to fly this altitude?
See one and two above.
*Why do jet a/c fly as high as possible?
Possibility of optimal fuel consumption and preferential routings together with higher TAS.
*If turboprops are more efficient a/c why do they not climb that high?
To be efficient at altitude, you have to fight the effects of compressibility. This means thinner, swept wings, more sophisticated propellers and heavier airframes to deal with higher cabin differentials. This would remove some of the operating advantages of turboprops. Additionally, at FL250 and below you don't have to have drop-down O2.
*What would you do if you had a radio failure on take off?
As Diaz pointed out - standard radio failure unless local and national procedures indicate otherwise. But carrying on with what you were cleared to do and squawking 7600 would be a good start.
*You are on a flight from Stansted to Amsterdam and just after T/O are at your cleared level of 2000ft when you have complete radio failure. What are your actions?
As above.
*Which is faster, London to New York or New York to London? Why?
See Diaz's post.
PM