I need to replace a shower arm for a mobile home bathroom shower, how can I open the wall or find access panel?

You do not need a access panel to reach a shower arm, (see image) You simply unscrew it. Are you sure you mean "shower arm" or is it another part you're referring to? Back to you, Tom

I unscrewed the shower arm, however the pipe or whatever seems to have fallen in wall, so I need to get to it.

The shower arm connects to a drop eared ell, (see image) which in turn is on the end of a pipe called the shower raiser. That's what you've lost, Take a coat hanger and put a hook on the end. Now go fishing! Don't forget to Teflon Tape the threads on the shower arm before installing. Good luck Tom

Unfortunately, you may have to open the wall. If the ears have disconnected from the studs, it is going to be hard to get enough pressure to screw in the pipe without it twisting. Sometimes you can pull the fitting up and screw the ears back through the wall. When the home was built, the plumbing was put in and the wall closed. You can cut the wall open, fix the piping and then put the paneling back and/or hang a door mirror over the opening.

My shower arm don't connect to that. Mine is plastic and it don't have any ears on it to mount to studs. Mine is held through the drywall with the trim ring on the front and a nut with a large washerup against the backside of the wall.