I liked it way more than Star Trek 2009. Had a few issues as a long-time Star Trek fan but nothing major.
Also, if you mean the warp core is essential to run most ship systems then yes it's now a primary power source. Though, in the prime universe it was used simultaneously with the impulse engines to power the ship. I also thought it was strange for them to make such an easily targetable system to be the main power source.
Also one of the writer's addressed your second point about the villain, JH, and said that that was a possible explanation.