"...I have a feeling that things are about to get a whole lot wilder."
At the beginning of the novel, this line sets expectations for the rest of the book; Cell 25 was far from the worst that the Elgen can bring. At the time of this quote, Michael only knows that he is about to embark on a mission to retrieve his mother; he has no idea how applicable this message truly will be. This is an example of an instance where a character says something that is truer than he can possibly know; the author is playing with perspective here, having the reader grasp something beyond what would have been going on in the character's mind.
"Their motivation is profit. But our motivation, our cause, is nothing less than a new world."
In this quote, Dr. Hatch is explaining to his pupils the difference between the board of Elgen, Inc and himself. For them, the experimentation with electricity in altering living being is and was solely a business venture, the results of which might be used to make a profit and expand the company. For Hatch, however, it is a more principally driven, noble endeavor: he wants to change the world and remake it in his own image, not unlike the Nietzschean Zarathustra. Rather than letting the matter rest now that his discoveries have reached economic success, he would instead like to continue his "research" and separate his eagles from the chickens, putting them in charge of this brave new world.
"Everything will be okay."
At this point in the novel, Jack has just returned home to find his house a smoldering ruin. Michael is trying to comfort him, but the quote has a deeper significance. It represents the necessary mindset of Michael and the Electroclan: they have no idea if it will actually be alright, or even if any of them will survive; they just have to tell themselves that in order to make it through. As Michael thinks after he says these words, "I didn't really know if what I'd said was true, but just saying the words helped me believe they might come true."
Rat power. In a bizarre way it made sense. Like my mother was fond of saying, "whatever works."
"Whatever works" could be the motto for the Elgen; they will do whatever they can in order to achieve their goals, stopping for no issue of legality or morality. The rats are a good example of this selfish trend; rats are low, nasty creatures, and their representation as the heart of Elgen's income and success was likely no accidental connection. By associating the Elgen with rats, the author is drawing a negative connotation in the reader's mind: they are vulgar people with an unprepossessing hunger for power, and they will do whatever works in order to obtain it.