I am taking the existence and stability of the rings for granted. You can figure out how it keeps together.
First, the presence of a ring system indicates that there is no moon, because a moon's gravitational pull would pull in any debris within it's orbit, which is where the rings would be.
Without a moon, and with a ring system, the amount of impacts from space crap would be staggering, causing a more or less permanent winter from all the dust in the air (that's an interesting idea for a campaign setting...). Civilization will most likely be concentrated underground, where it is safe from the constant bombardment of the falling space debris, with the surface world being a dangerous, frozen world where only the brave dare enter venture.
If the ring is perfectly in line with the plane of the planet's orbit around the sun (not the axis., as indicated in your second point, instead of a thin band in the sky, the area north/south from the equator for about 2-3 miles would be in a permanent state of total solar eclipse (sort of a desolate, barren darkness across the center of the planet, that's a cool campaign idea as well!).
On your point about the axial tilt causing the rings to cast a shadow. During each day, there would be two periods of night lasting about 1-3 minutes depending, on one's position on the planet, when the sun crosses behind the rings.
Here's a idea of the world as I see it. The rings were created during a time when civilizations were present on the surface, the planet would be covered in ruins buried in ice that were abandoned as civilization fled the surface, a great place for a party of adventurers. Surface flora and fauna will have adapted to the drastic environmental changes. Burrowing creatures will have survived because they can take shelter underground and will have taken a role in many ecological niches that were left empty. Everything will be adapted to survive in sub-freezing temperatures (Layers of insulating hair/fat, etc.)
I really want to go on, but I probably should quit while I'm ahead.