That's still a matter under dispute. There is no know mechanism that would cause it, but some studies suggest that holding the phone up to your head when it's in use could cause brain cancer. I've also heard of a study (only one) suggesting that keeping the phone in your pants pocket can cause sterility. So, maybe it can give you cancer, but it's not really obvious that it can.
Oh I hope not! There have been many studies about this, and most of the results are inconclusive. Everything seems to give you cancer. We live in a world of chaos with so many ways to get cancer. I think it's a risk I'm willing to take.
Ugh I hate this rumour. No, it won't do anything. And it's the same for putting it other places, if you put it in your hood it won't give you a brain tumour, if you put it in your bra it won't give you breast cancer