1. You don't need a spare rudder. All boats with cable steering, though, need an emergency tiller in case a steering cable breaks. There should be an opening or fitting of some type in your cockpit sole to allow you to insert an emergency tiller into the top of the rudder shaft.
2. If the steering cables look good, take a wad of kleenex (to protect your hand) and run it over the entire length of the cables. If it catches on a frayed cable, even a single strand, replace the cable. If you can do this and there are no frays (also called meat hooks- that's the reason for using the kleenex) anywhere, then you can skip replacing the cables.
3. Are you aware that there is an Islander 37 association online? http://islander37.com/
They have a forum and you may be able to get some more specific info there.