Hi there.
(1) No; there isn't a general forum for all courses unless you make a course and enrol everyone on the site in it.
(2) Students by default should be able to create a new topic in the forum but NOT if you are using the news forum which appears at the top of every new course in Moodle. Turn on the editing and click to add an activity or resource and add a forum elsewhere in the course page -use the standard forum type. Also, please see #1 in Forum FAQ