Is there a way to mount my Android phone on my Mac Air desktop in order to transfer files like images and music?
Use Android File Transfer, created by Google itself, and it gives you a Finder window to at least transfer files via USB connection. I noticed, however, that you have to use the Samsung cable they provide to power the phone, and not some cheap knockoff USB cable.
It would be nice to have a way for the icon to mount on the desktop via a Bluetooth connection -- but that's just not possible yet.
There is also the free Handshaker application in the Apple Store that is more full-featured and intuitive than Google's Android File Transfer. So far, it's looking like my best option and I don't see quirks except that I had to enable Android Developer Mode and then turn on USB Debugging on, as well as uninstall Android File Exchange because it conflicts with it.
It is possible to use "Android debug bridge" (ADB) command line tool. It is intended to use it for testing and deploying apps under development, however it enables users/developers to run commands like
adb ls to list all files and
adb pull sdcard/DCIM/Camera ~/Documents/ will copy all the files in the sdcard/DCIM camera folder to Documents. Read more on how to install and use the tool here. Note adb requires the phone to have enabled developer mode and USB debugging. Read more here; https://developer.android.com/studio/command-line/adb.html
Still, if there was another app to accomplish this, it would be much better as this official app hasn't been updated in over 5 years. Also, handshaker has recently broken. (At least for the time being)