1) Yes. After you die, your will is filed with the probate court and becomes a matter of public record. Anyone can get a copy of your will from the court. In addition, any filings in your probate estate are public record as well. This is one reason why people use living trusts to avoid probate.
2) It's amazing how much power Hollywood has. "Will readings" are, for all intensive purposes, a Hollywood fiction. This does not happen in real life and is certainly not required anywhere that I know of. If you are referring to a probate hearing (at which I can't imagine the will is read aloud), then sure anyone can probably attend if they wish, but they aren't usually that exciting. The probate estate is usually opened shortly after death, but at least in Illinois, there isn't a time limit, and in fact if an asset is discovered years after death, a probate estate may then be opened or re-opened if needed.