Regarding PTT, it’s a real Push-to-Talk function over cellular network. It’s a function that was present already even in some venerable Nokia phones, like the 3110.
The description of the F570e liked above reads:
“Fplus R570E is an industrial secure smartphone for corporate use based on the Russian mobile OS Aurora. The IP68-rated device with a dedicated PTT button is designed to automate the work of mobile workers in the harshest environments.”
So, it looks like the device hasn’t been designed just as an average smartphone for the general public, but with a particular target of industrial workers.