Do the First Amendment's protections to public streets as the archetype of a traditional public forum extend to city and state public streets and public buildings owned by a public university?

QUESTIONS PRESENTED 1) Do the First Amendment's protections to public streets as the archetype of a traditional public forum extend to city and state public streets and public buildings owned by a public university? 2) If indeed the First Amendment's protections do extend to the public streets and public buildings of a public university, is the public university required to provide Fifth Amendment Due Process for deprivation of that liberty? 3) Does the Eighth Amendment's provision for proportionality apply to an 18-month ban from large swaths of public land, streets and sidewalks across the state of Oregon, owned by the public university, for merely falling asleep once after hours in a library, without any mention of threat to property or person?