Can I choose the open Wi-Fi channel? My MBP's Wifi connection is very slow. How can I know if I am connected to the best available channel and can I choose the one channel instead another?

I do not have access to this "public" router.

This is what Wifi Diagnostic tool looks like:
you can't select the frequency that you connect to any specific router to unless you have access to the router.

It's like (literally) "can I access my favorite radio station on 88.5 instead of 102.7?" It is the base station that determines the frequency (channel) it transmits/receives at.