A) If you don't want to risk putting it in your pocket, or it wont fit, your only other option really is a lanyard. You can pick one up on most sites that sell supplies.
B) It's not suppose to leak and I haven't ever had one do so. It seals at both bottom and top when the drip tip is put on. You should be able to tilt it and hang it upside down and no fluid should leak anywhere. If it is, something is broken.