Is there a way to include a "Print" button/icon/menu option -post specific- that would allow me to print a post (topic & all replies) only, without forum menu, side widgets, etc., which do get printed when I use browser's Print option?
I'm sorry, but this requires custom coding and there is no simple solution I can post here. I'd suggest you use some additional plugin, e.g. Print, PDF, Email by PrintFriendly. As far as I know, the plugin allows deleting the unnecessary parts before printing.
Here you'll find more options: https://wordpress.org/plugins/search/print/