The idle stepper motor would seem to be an obvious cause of the problem, but look at doing things like cleaning the throttle body and making sure there are no vacuum leaks, which can sometimes cause a high idle speed. If you want to get it checked take it to a mechanic, the problem is more likely to be mechanical than electrical.
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It is common for cars running E10 fuel to be a little more difficult to start than they are on regular unleaded. Try unleaded and see if the problem persists. A rotten egg smell is usually a sign of a problem with the catalytic converter.
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DIFFICULT to apportion blame here. When they talk about the belts, were they talking about the cam timing belt or the external belts? The cam belt needs to be replaced at the carmaker's service recommendation. If that wasn't done, then you probably have a claim. If it was changed and it subsequently broke, you probably don't have a claim. You need to check your paperwork and see if it refers to a manufacturer's logbook service. You should also check for a guarantee, because most service people will back their work with a warranty.
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