Hello and welcome to Just Answer.
With your car being an 03', your new car warranty is expired. If you give me the last 7 digits of the VIN number, I can see if you have a BMW extended warranty.
1. More than likely the water drains for the top storage compartment are clogged and the top hydraulic pump got wet. The pump will need to be replaced and to do so the entire convertible top will need to be removed. This is not something that can be done by an untrained technician.
2. Sounds like a door lock actuator failing. Reletively common. Sort of difficult to replace because the regulator will need to be removed to replace the actuator.
3. The steering should get stiffer in sport mode, this is normal.
You are in luck! Your vehicle has a "certified pre owned" warranty from BMW. This warranty is set to expire 07/28/09 so you need to get it into a dealership befor that. They should cover the top repair and the lock actuator and only charge you a $50 handeling fee.
Anything else, feel free to ask!
Please do not forget to click the "accept" tab if my answer is helpful to you.
BMW Master technician
BMW S.T.E.P. graduate, 10 years BMW dealership experience