What kind of a bathroom vent is this? How do I open it?
We have a fan like that.  The external body pulls straight down a couple inches and hangs on a pair of wire, spring-like supports.  From there, you can access the light bulb and a bit of the fan.

I haven't done it, but from there, I would assume you can remove the fan and get a look at the vent pipe.  For us, the alternative would be to attempt to access from above via the attic.  That may be an option for you.