I am 100% civilian, so forgive my ignorance in advance.

1. You are at an initial meeting with a very influential sheik. He asks you why you are here and what you are trying to accomplish. How do you respond?

Offer to show him. The political science literature makes it clear that to humans "talk is cheap", this is even more true in a conflict environment. Anything you say will carry minimal weight. The alternative is to send a "costly signal", meaning take him around and personally show him the tangible humanitarian / stability projects you are currently undertaking.

The benefit is twofold. First, you send him a "costly signal" that you mean business and am capable of going beyond words. Second, your reputation is boosted by being seen with an influential sheik.

2. During your meeting an explosion happens up the street. In route you are intercepted by a journalist. He asks you about the explosion. How do you respond?

Once again, offer to show him personally. Reporters write their stories with limited information. If the only quote he has is of you saying "there has been another explosion by unknown groups" you can be pretty sure the tone of the story will run long those lines. However, if he accepts your offer there is a greater probability he will write about YOUR ACTIONS ("US Quickly Secures Bombing Site and Treats Civilians") rather than the EVENT itself (Another Bombing in Samara").