I started minecraft last week to play with my kids. I built a huge castle in the sky between 2 hills. When I was just finished I find something walking around the courtyard (all door were closed). I rushed it with a pickax, pinned it against the wall and clicked as fast as I could. I spent 2 pickaxes and didn't seem to do any damage. Now I'm dead and it standing over the bed and chests inside the castle courtyard. I look it up and find its a witch, but there are no comments on special tactics on how to kill it. Its supposed to be a simple thing?

How did it get into my fully lit and walled castle? Can they fly or jump? Open doors? Go through walls? Why won't it die? I need to be able to keep monsters out. Castle design:

                                                                __
|_______                        ____________________Witch__|   /
        |     castle            |                             |
        |            ___________|                             |
        |           |                                         |
        | respawn   |                                         /
        |___________|                                        |
       /             \                                      /
      /               |                                     | mountain 
     /                |

P.S.: I found out building a canopy over a valley is a bad idea. Shading that much area brings out a non-stop barrage of creepers and skeletons making going out a death march, not to mention un-passable, unless one brings a full load of dirt to climb out of the sheer number of blast craters.