The buzzer is your seat belt warning. If you do your seat belt up before turning the ignition on you'll find it dosn't do it.
I just disconnected the wire that goes to the seat belt catch in mine, that stops it
The heat light, as has been said, is to do with your cat. The early Roadsters didn't have CO2, or lambda, sensors. Instead there was just a temperature sensor in the cat to show when the cat is overheating (I think). From what I've read these go wrong after only very low mileage and isn't really needed anyway, all it does is bring on the warning light. If you can get underneath you can see the sensor wires coming from the cat and there's a connector. Just disconnect this and forget it. Mine already had this disconnected when I got it and I then had to do some research to find out what it was for.