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The charge regulator on the Mayfly circuit board has a maximum output of 500mA, so even if you put a large 6-watt panel on the Mayfly, it’s still not going to charge it any faster since you’re limited by the 500mA charge regulator. But in areas with lots of shade, using a large shaded 6-watt panel can give you the same results as using a smaller panel in full sun.
The yellow LED on the Mayfly indicates that the battery is actively being charged. Once the battery is fully charged, that LED goes out and there’s no other indication that the battery is full. The Mayfly can sample the input Lipo battery voltage on analog input A6 so you can print it to the serial monitor or write it to the card or whatever. There’s an example sketch on how to do that here: https://envirodiy.org/mayfly/software/battery-measurement/ If you’re needing to know Lipo battery voltages often and when not connected to a Mayfly, then there are small Lipo voltmeters you can get, just be sure to observe polarity since many of them have reversed pins on the JST-2.0 jacks.
And yes, the Mayfly will charge your battery even if the power switch is turned off. You can also charge a Lipo battery by connecting the microUSB cable of the Mayfly to your computer or just use a regular phone charger.