Look at "b" in your post.
Yes and the burden is on Zimmerman to present evidence to prove (b) was indeed the case. Whether Zimmerman meets this burden is for a judge to rule on, not the police.
No, innocent until proven guilty, not guilty until proven innocent.
When you assert an affirmative defense the burden is first on the defendant to prove he was justified in using deadly force. It then becomes the state's burden to prove the defendant's evidence doesn't meet the legal standard to mitigate murder.