Problem 1 - when you bridge it does not merge the edges on the sides. Go to the polygon display options and turn on display border edges and make them thicker and you will see you have open edges after the bridge. A better way to do this in Maya, especially for just filling in one missing polygon is to use the Fill Hole command.

Problem 2. Maya axis orientation does not work anything like Max. If you want to change the orientation to normal to the selection goto the tools tab and and you will get several options including normal to selection.

Problem 3. I do not have access to Maya atm so I cannot recall if there is an option in the tools tab for scale to align to edge. You may have to use the parenting trick. You align a cube to the orientation you want and then parent your object to that cube and then reset the transforms on the object. It's local axis will now be aligned to the cube. You can unparent the object and delete the cube.