The anterior cingulate cortex (ACC) is a brain region involved in feelings related to choice (cf. Walton, M. E., Devlin, J. T., & Rushworth, M. F. S., 2004. Interactions between decision making and feedback monitoring within prefrontal cortex. Nature Neuroscience, 7, 1259–1265; Legault, L., & Inzlicht, M., 2013. Self-Determination, Self-Regulation, and the Brain: Autonomy Improves Performance by Enhancing Neuroaffective Responsiveness to Self-Regulation Failure. Journal of Personality and Social Psychology, 105(1), 123-138). An increase of activity in the anterior insular cortex (AIC) related to feelings of agency was found by Lee, W., & Reeve, J. (2012). cf. their paper: Self-determined, but not non-self-determined, motivation predicts activations in the anterior insular cortex: An fMRI study of personal agency. Social Cognitive and Affective Neuroscience. Advance online publication. Murayama, K., Matsumoto, M., Izuma, K., & Matsumoto, K. (2010). cf. Neural basis of the undermining effect of monetary reward on intrinsic motivation. PNAS: Proceedings of the National Academy of Sciences of the United States of America, 107, 20911–20916. have demonstrated that activity in the anterior striatum and prefrontal cortex is reduced when intrinsic motivation is undermined.
I would start with the prefrontal cortex. It controls, and is involved in all four aspects you mention in self-determination. It invokes the use of many other parts of the brain, but it is the controller. Read the book: The New Executive Brain, by Goldberg.
The dorsolateral prefrontal cortex is important in emotional and psychological balance. In addition, the limbic system generally, including the amygdaloid complex and the nucleus accumbens are crucial in these behaviour.
L. Levita, R. Hoskin, and S. Champi, 'Avoidance of Harm and Anxiety: A Role for the Nucleus Accumbens', Neuroimage, 62 (2012), 189-98.
For item 1, I would second the ventral striatum for both motivation (c.f. John Salamone literature in rodents; Brian Knutson in humans), For item 2, same structures (c.f. temporal difference reinforcement learning literature in fMRI such as John O'Doherty and Nathanial Daw), For item 3, computational modeling literature such as Valerie Voon, that also implicates the dopamine circuitry, and for 4, pubmed 21931157 and related citations.