I have to kill a couple mice every week, no pre-killed frozen in Taiwan! Here's how: mouse goes into plastic bag, bag quickly rolled around it (so you can see where it's head is) then whack head-end of bag against a hard horizontal surface e.g. table. Don't be a total wuss about it but don't try and smack a hole through your table either. I've gotten pretty efficient about it and the mouse is only alive in the bag for about 5 seconds.
There are other methods you can do a search on, like cervical dislocation and mini gas chambers. Much as I need to kill the mice I want to prevent suffering as much as possible, and I'm not sure enough about the cervical dislocation enough to want to experiment on some poor rodent. I'm sure someone will be along soon to rant about how inhumane and horrific the bag-and-whack is, but in my experience the mouse literally does not know what hit it.
As to the bite on your snake's head, you are very lucky the mouse didn't do more damage and I trust you won't be leaving a live mouse in with your snake again. You can dab neosporin on the wound. Remember live mice are going to fight for survival, if a giant monster was coiling around me I'm pretty sure I'd resort to biting it too.