I have only 1 paid app. The free version of it has around 60,000 downloads, the paid version around 600.
I was going to say I never used copy protection because I never thought anyone would want to pirate it but I just had a wee google and low and behold it's posted on several forums and loads of those blog websites that seem to copy from each other.
Obviously you can't get download numbers from the filesharing sites so who knows how many times it's been pirated. To be honest though, I couldn't really care less.
As someone who does this as a hobby rather than a job it doesn't really effect me all that much and to be frank I'm kind of complimented anybody would want it that bad they would pirate it and that several different "groups" took the time to make it available. I do like the fact they all claim to have cracked it though. There is literally zero copy protection so what is there to crack? But I digress.
What I will say is if someone wants your app without paying for it they will get it. My silly little app has been pirated so anything of actual worth will be too.
As for the permissions, I've found as long as you explain it on the market most to all users are totally fine with it.
Tl;dr pirates are gunna pirate. It's inevitable. Also, most people don't care about permissions.