1: EPR or N1 for T/O, depends on engine manufacturer, is a measure for the amount of thrust given. EPR will decrease because of the ramrise, ie once you start moving and accelerating you will have more air coming in the engine
2: VMCG always have to be lower or equal to V1, otherwise you can have controlability problems when you loose an engine. it is possible you calculate a lower V1, but in that case you will increase to at least VMCG.
3. NO, Jet airplanes usually do not have a critical engine, that has to do wiith prop aerodynamics. However, I hope you understand that on the 747 the outboard engine failure gives more swing because of the arm.
4: D rated thrust: a jet engine has a max thrust rating, since we operate from long runways, iso giving max thrust and a short T/O run, we will use the whole runway to calculate a lower thust setting. this lower thrust setting is the D rate. we do this by fooling the engine and putting in a higher temperature in the computer ie a higher temperature than the flatrate temp. otherwise you still get maxT the assumed(boeing) flex(airbus) temp give the dvantage of lower EGT in the engines->longer engine life, it does cost more fuel to do a derate climbto cruise level.
hope this helps, it was typed at high speed so ther are spelling errors. probably more people will expand on your questions and my answers
The following sources are readily available and have the answers you seek....
Handling the Big Jets D.P. Davies Flying the Big Jets Stanley Stewart Aerodynamics for Naval Aviators H.H. Hurt, Jr. edited by US Federal Aviation Administration
Once you have studied those, then the following is a useful source of interview tech questions, although it contains some, ahem, imprecise explanations -- to be fair it does not set out to be a text book:
Ace the Technical Pilot Interview Gary Bristow.
The above are all useful for your purpose, and they will continue to be useful resources during your career. All are readily available through Amazon.com and pilot shop websites all over the world.
FWIW, the 'quick and dirty' answers to your questions can be found on pp75-79 of Bristow, but if I were you, I would use Bristow's questions to check your knowledge after studying the other texts. Cathay interviews are notorious for their focus on technical knowledge. If you are serious about your CX interview, you should have your head in those books and not rely on answers you got on PPRuNe!
Also, FWIW, the term is "derated" thrust, which is a fixed amount of thrust reduction used for takeoff to improve engine life. Depending on specific airplane, engine, and airline, fixed derates may be used instead of variable "reduced" thrust.
For fixed derates, check the book to see if you can take off with the desired derate (usually 2 available), push a button, and the engine or autothrottle computer automatically calculates and sets the selected (nominally 5-20%) derate. For variable reduced thrust takeoffs, the engine setting (N1 or EPR) has to be calculated for each takeoff.