Nope. water should be warm but wetsuits do give added bouyancy and help improve your form you could rent one from a local tri shop or maybe the race director can direct you if you felt compelled to.

Depends on the temp. of the water and how comfortable you are with swimming? I prefer to wear one for the buoyancy as well as keeping the cold water off of my skin. It helps keep your muscles warm for the bike instead of starting out with cold muscles. Again, that will depend on the temp. of the water. I agree that you should rent one and try it out before your race - do not wait until race day especially if you've never been in a wetsuit. I did two open water swims before my first race and was very greatful that I did. I've now purchased a wetsuit because I can't imagine racing without it.
Most importantly - have fun!