Questions about the last Start Trek Movie

I enjoyed the last Star Trek movie. I just had a few questions I was wondering if anyone was able to answer (better late than never):

* How are they able to go through a black hole?

* If one drop of red matter can make a black hole, why did the logical Vulcans make enough to take a bath in and put it all on Spock's ship?

* Why was it necessary to use a drill to deliver the red matter? Would the black hole have bounced off of the planet if they didn't drill first?

* If the Romulan had the red matter and was thrown back in time with the foreknowledge of his planet's destruction, why didn't he use the red matter to save his planet? Did he not care about his planet?

* If warp speed is faster than light, why wasn't the Enterprise able to fly away from the black hole?

* How is a slower than light explosion able to push them away from the black hole?

* If the Enterprise ejected their core, wouldn't they just lose warp power and fall into the black hole? Or do they not need their core to maintain full power? If so why do they have a core?