PhpStorm does allow you to access a command line from within the IDE. Off the top of my head, I think the shortcut is Opt + F12. Keep in mind if your command touches the database, you won't be able to use it from your local machine as opposed to the Homestead environment, unless you're using a SQLite database.
You mean running the commands from PhpStorm directly? I haven't seen this functionality. They're just run on the command line, which you can do from the built in terminal.
I don't think PhpStorm will be able to execute the commands within Homestead as that would require it to SSH into the box to run the commands. If you don't have PHP installed locally, you can't run the commands locally.
I installed php internally however the setup which was mentioned is not working. Are you able to follow the steps and able to execute artisan commands ?