1. First of all you are going to be really frustrated if you try to make 1-to-1 comparisons to the way max does things and the way maya does. You just have to try to adapt and try to be flexible or you are going to be very unhappy.

Technically maya's bridge does merge the edges that you bridge between. It just does not weld the edges that happen to be on the ends. See the screen shot below.

Maya's bridge offers some options that Max's does not. For instance you can bridge following a curve (see the Bridge tool options).

To fill a hole in a mesh Fill Hole is a better choice in Maya. Another option is Append to Polygon. there are almost always several ways to accomplish the same task. You just have to adjust to Maya's workflow and not try to force it to be Max.

2. reset the tool because it should put the manipulator at the center of the selection (see screen shot below)

3. There might be a script. You can create a script or plugin to do just about anything in Maya. There are lots of sites on the web to find maya scripts a good one to start with is Creative Crash (https://www.creativecrash.com/).