Well, I usually pronounce it with a soft /s/, because it's just one of those words that's hard to unmap in my brain... but yes, "Zeus" is a very good approximation of the correct pronunciation. Just make sure you're pronouncing the ü correctly. You form your lips much more like you're going to pronounce English long U but inside your mouth you pronounce long E.
In real life, I usually end up saying Zeus with or without a sharp /s/ and no one's ever misunderstood me. So work for the ideal but don't be afraid to get out there and talk. :D
No, there are rules for which one to use, and the rules changed in 1998 with the Schreibrechtreform. For example, for "essen" I learned to write "er ißt" but now it's "er isst". So do your best to memorize where there's an ß--it's important. And if you think of it as "ss", then you won't have any problems with variant spellings.
However, if you are on a typewriter or computer without any way to type an ß (greek β works in a pinch on a typewriter), "ss" can always be used. Capital "ß" is also written "SS". In very old documents, you'll see that ß was typed "sz". It's really rare nowadays, but now you'll know it when you see it.
As long as we're talking about shortcuts, ä, ö, and ü can be spelled "ae", "oe," and "ue" as well. The rule is that you should always use the accented characters when it's reasonably practical, but if you cannot, then the above substitutions are always perfectly legible to a German speaker.