On your second one, I would argue they don't use what ever is handy. They come prepared. They are going "to work". They don't leave home with items they need to do the job properly.
Claim 2 and 3: I agree with you 100%
you made some excellent points. but just wanted to clarify that when i said "they use whatever is handy", i didn't mean that they turn up to the crime scene and hope there is a weapon lying around they can use. I meant, if they have a hammer at home and feel comfortable wielding that, they will use that. if they have a gun lying around they might use that. all i meant was: the use of a hammer does not NECESSARILY indicate a personal crime. sometimes hitmen are lazy. sometimes they don't have money for a gun.