You could have just used Laticrete and set the tiles straight over the existing laminate. For the step, they sell precut transition strips, or, you can just buy a general peice of quarter round wood and cut it yourself, much cheaper. Or bevel caulk it.

I used to do tile for a living.

That black thing in the door is called a thresh hold, it is removable, or at least cut that nasty caulk out or it will look like hell. Also, for the trim, you don't need to remove it, just get a jambsaw or a peanut grinder and cut it up half an inch or so. Use caulk where the tiles meet any perpendicular surface.