1. Gin discovered that Aizen was the one responsible for the attack on Rangiku, and thus vowed to kill him. It's somewhat implied that Gin loved Rangiku, since he never made any attempt to kill her, he simply incapacitated her.
2. Aizen's true motives are quite controversial. There was the possibility that he truly sought to find someone stronger than himself, so that he could be an ordinary Shinigami, but that doesn't make much sense. There is the possibility that he tried to kill the Soul King because he might have been something only Aizen knew about, and nobody else did. The most likely one however, and the one that makes the most sense, was that he wanted to become God. A number of quotes from him imply this.
"No one stands on the top of the world. Not you, not me, not even gods. But the unbearable vacancy of the throne in the sky is over. From now on...I will be sitting on it."
"It is the nature of all living things to find some being greater than themselves and place their trust in that being, following it blindly. In order to escape from the pressure of that trust, those beings seek a still greater entity in which to believe, and those greater beings too seek still greater, still stronger beings to follow. This is how all kings come to be, and this is how all Gods are born. Do not trust in me yet, Hirako Shinji. I will take my time to teach you the nature of the God whom you face. Then, you shall believe."
"Fear is necessary to achieve evolution. The fear that, in one's current state, one could quite possibly be destroyed at any time. I thank you, Gin. It is thanks to your presence that I have finally succeeded in surpassing both Shinigami and Hollows."
The first one shows this better than the other 2, but all of them have relevance to his "true" motive. He most likely saw the Soul King as a faux God, a being unfit to have the position of God bestowed upon him. Aizen is a power-hungry man, and he feels he is entitled to the position of a divine being, and nobody else fits the position better than himself.
