shaky idle, power loss

[YarisTY]

Greetings everyone! '08 Yaris 3-door.

I use a voltage meter in the cigarette light to look for a possible alternator problem. Normally, when idling, the engine is smooth, quiet, and the lights on the Voltmeter stay orange/green for the alternator. However, it now has this thing, at times, where the engine vibrates, causing a rattling noise, and the two alternator lights on the Voltmeter go off completely. The lights come back when I rev the engine. (I assume the lights mean that the Alt is generating a charge.) No check-engine light at all.

Friday, when I had the voltmeter out all day, the dashboard's low battery light came on. I put in the meter, ...zero lights for Alt, battery on orange/red. pulled over, checked everything, disconnected, reconnected, restarted a few times. No change. Made it home before dark. Turned off, restarted, no change. 15 minutes later, I started it one more time and PERFECT! No low battery and all light on voltmeter on, including the Alternator. It did this about 4-6 months ago and I eventually changed the alternator (since it was the original at 206K). I figured a sporadic failing alternator. Also, a new battery with more power. No problems until now.

How can the car dash show a low battery and then minutes later..... NOT?
What causes the low idle vibration? Why does it cause the Alt lights to go out?
Does the lack of Alt lights on the voltmeter mean it's not working or is it a false reading?