Hello, I'm Chris, a current Ford Lincoln Mercury employee.
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Both the alternator and battery need to be correctly tested. You also do not need to remove the battery cables while running this will create power spikes which can ruin the PCM and alternator. With your symptoms it sounds like a faulty battery. Also check the battery cable connections. If you did not use a motorcraft alternator then expect it to fail sooner than later.
All the warning indicators your getting are occuring from Vbatt loss meaning your getting under 12 volts.