Stolen iPhone 5c

My iphone 5c was stolen on saturday night. Whoever stole it turned it off. Once I realized it was stolen I got on a friend's phone and tried to locate it but since it was off it was "offline" I couldn't track it. I didn't have a passcode on my phone so the thief could have gotten into it but I guess they just turned it off. I don't know

I know I had the iOS 7 and the Find my iPhone turned on. I've also checked my carrier's account and no minutes or texts or anything has been used. I also never recieved any emails about any of my passwords being changed or Find my Iphone being turned off or anything.

So my questions are:

Do they seriously just have my iPhone and have it turned off?

If they turn it on could I still find it ? or could they have turned off Find my Phone?

If they have it what can they do with it just turned off? (take out the sim card?)

Is there still hope?

I really don't want to give up hope by getting a new phone and being out ~$500...but I've also been without a phone for 4 days now and it *****.

Any advice?

(I've filed a police report but I doubt they do anything.)

This is SO Frustrating!!!!

Thanks for any help.