old 12v dc phone and device chargers/adapters

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officework13

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thanks to all who may be able to assist me. i am new to this forum and would be a liar if i said i was anything more than a beginer electronics hobbiest. however, i do understancd some basic concepts of electronics and can solder, which does nothing more than make me a dangerous electrician.
So, after several years, i have accumulated many different 12volt chargers/adapters for phones, mp3 players, fm transmitters, cameras, etc. and each one seems to have a different plug in adapter (for the applicable device). and i believe they all indicate the output (i.e. 9v, 600ma).
Here are a few questions which i will number, so if you respond to a particular one you can indicate which number it applies to. (note i am trying to power a 9V, 500ma device and my powersource is a 12V 5ahr gel cel battery)

1. using a fully charged battery and using the full power draw of the device, how long will the battery last. (i am thinking 10 hours - in the most simplistic way 5000/500=10).
2. if i have a 12 volt converter/charger that has an output of 9V 600ma, will this be adequate to run the d evice.
3. what happens if the if 12 volt converter/charger had an output of 9v, but the amp output was either higher or lower (i.e. low-400ma high 1.5amps). i expect the device will not work with the low and possibly fry the device with the high). if this is so, could i put an inline fuse in to prevent it from frying the device. what size fuse would i use.
4. to recharge this 12V gel cel battery in the field (from my vehicle could i simply plug a lighter socket plug in and attach the 2 wires to the 12 V gel cel battery. will it overcharge or just equalize to a max of 12-13volts.

thanks
 
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