Many of them shrink when they solidify. For the size and tolerances needed for a ring you can probably ignore this detail. You can get what is called a low-shrink mold made for some alloys that helps mitigate this if you want to make your prototype to finished size (or you didn't know better before you takes to the jeweler).
Patternmakers deal with this using what are called shrink rules. They look like regular rules, but are e.g. 5% longer. If you're buying an old rule, make sure you don't get one by mistake.
Silver rings, worn regularly, won't need to be polished to keep the tarnish at bay; the contact from your skin will do quite well enough. Our wedding rings are also silver, and I've only polished mine when I haven't worn it for a while. Ours probably don't polish up to quite the same luster though. They're a regular alloy of silver for jewelry and not silver and gold.