Connections Air filter box

moin, on the air filter box lid of my 850 2.5 10V 1996 is probably a “low pressure (?) connection” broken off, see picture. A very thin, black “tube” hangs loosely around in the area…. 1) What is this hose for? 2) is there a replacement for the defective connection (on the side a “plug-on tube” broken off)? 3) can this connection be changed at all or do I need a new air filter cover?