first you need to check for any vaccum leaks. If no leaks are found look too the IAC ( idle air control ) some times you can tap on the IAC while the engine is running causing a change in the idle if so you should change the IAC.
yes the clock remains on, otherwise you would have to reset it everytime you restarted your car
A PLUGGED CAT. CONVERTER
Yes
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The fan relay could be bad or the fan motor could be bad.
Possibly some leaves have entered through the fresh air intake.
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