Hm, in order. Yes it does, no she doesn't have to be aware of it, though that certainly helps, and theoretically she could. It just may look to other people like she's stupidly lucky, since it operates more on a subconscious level than anything.

It doesn't work off intentions exactly, so it would still work against a thing incapable of what we would consider rational thought. Not really, she could tell if it was going to shoot at her seconds before it does so, but overarching intentions, nope. And yes, if an object were to become an impromptu weapon, she could theoretically dodge it. 

Essentially it's kind of a fusion. Besides certain major events (For example, World War 1, which was going to happen one way or another, just with the details different), the future is constantly in flux. What she 'sees' with her precog, is events when they have become solidified enough in time that they are going to happen, whether that be getting shot at, or someone tripping and falling on their face. The latter she would only see like a second before you were actually tripping, too late for her to do anything about it, which limits it's effectiveness (Because we don't want precog to be OP), but not too soon for her to respond. On the battlefield, she sees where the attack is going to be a split second before it's fired at her, and dodges. 

I can RP it a lot better than I can describe it. Honest.