The 2500 RPM sounds pretty normal. It is going to idle high, until the engine gets warmed up.
The dying issue sounds like it could be a fuel problem (maybe the fuel pressure regulator) or a sensor that isn't adjusted correctly (maybe the TPS).
Can you download an FSM (factory service manual) from suzukiinfo.com? They are big files (several megs), so you need a high speed connection. An FSM will have all the troubleshooting and testing procedures you will need.
For the rough running. You could pull the plug wires individually start the engine and see if it runs any differently. If it doesn't, then whatever plug wire is off at the time will tell you what cylinder has the problem. Could be a valve, or valves, that aren't adjusted correctly, could be a bad plug or plug wire, could be the cylinder itself (like the rings aren't sealing correctly), could be an injector that isn't working right (make sure all the plugs are plugged in securely to them).