Will the planet Saturn look different than it does in a billion years?

Probably. Some evidence shows that the rings are relatively recent, so they may also be gone in a billion years. They are fundamentally unstable, being made up of millions of small boulders and chunks of ice.

No one really knows the answer to that question, but perhaps in a few years 1) computers will be smart enough to model a ring system over the long haul and give us an accurate prediction 2) we will have space telescopes strong enough to ":see" ring systems on exo-planets.

If they are common as dirt, which I think they are, then Saturn is probably pretty stable.

According to

http://www.space.com/20424-saturn-rings-moons-age....

the rings are very old. So they will probably still be there. I don't think we have enough information to estimate what kind of rates of change may be occurring. A billion years is a long time, and if current images could somehow be preserved that long, some kind of difference could be noticeable.

Yes, the rings have to be short-lived (only a few million years).