Check engine light on
#2
Get an OBD-II code reader (around $50 from places like Harbor Freight) and read the codes from the ECM and it should tell you what the error was (make note of the code # so you can look it up online). Chances are it was just something that got set errantly when you had the battery, etc, disconnected to change the alternator. If that is the case you can use the code reader to clear the codes and then drive the car around 20-30 miles and if the light doesn't come back on again you are good to go. If it does, then hook up your code reader again and go from there.
Places like Auto Zone will read the codes for you for free (many shops chare a fee just to read the codes -- often as much or more as buying the tool to do it yourself)... but it is much handier to have your own code reading tool.
Places like Auto Zone will read the codes for you for free (many shops chare a fee just to read the codes -- often as much or more as buying the tool to do it yourself)... but it is much handier to have your own code reading tool.