Where to place a binary file to make it executable from all apks on device? I have a binary that I want to make executable by all Applications on my Android device, just like the commands in /system/bin (ls, etc.).

What is the best way of doing this? Does it have to be in the /system/bin folder and does the device have to be rooted?
I cannot fathom what you're trying to achieve by doing this but you must mark the binary permissions executable for all. You can do so by using any Terminal App from PlayStore. Download any of them, fire it up, type chmod +x your_file_location

Otherwise, you may use ES File Explorer app from PlayStore, place your binary wherever you want, go to its properties, and change the permissions by selecting all x boxes.

And, you need to have rooted device if you want to place your binary into any folder other than of SD-Card or Internal Storage.