To answer all of that, one needs to know all (or at least most) of the devices available. So all I can give is an "educated guess".
Permissions should not be altered by symlinks. And yes, what's there varies across devices, Android versions and even ROMs used.
Find the "real one" using df or mount at the command prompt (either via a terminal app, or using adb shell). Starting with around Android 4.2, a few of your listed locations should be pretty much standard:
/storage/emulated/0
/storage/emulated/legacy
The others, as I wrote, may vary between devices, Android versions and ROMs.
Concerning read/write permissions: All of them have. Question is just: for whom? The average app, or root? This changed a lot between Android versions, especially since Kitkat, and again might be handled differently by device, Android version, and ROM. Before Kitkat, an app just needed the WRITE_EXTERNAL_STORAGE permission. With Kitkat, on most ROMs it was restricted to its own directory in Android/data/, and with Lollipop that changed again.
For a reference, please also see Confused by the many locations of the virtual /sdcard/.