Yes you sure can.
Two six volt batteries in series makes 12 volts so switch the charger to the 12 volt position.
You cannot do this. If it were a 36 volt charger you could connect three 12 volt batteries in series and charge all 3 at the same time. But this is a 32 volt charger which I have never heard of.
A twelve volt charger will charge twelve volt batteries only unless it has a feature that allows you to change the chargers voltage. But on fast or slow charge 12 volts is 12 volts so most 12 volt chargers are only good for 12 volt batteries.
The charger needs to be set to charge for the voltage that the battery is designed to produce. Most car batteries are 12 volt batteries.
You cannot use a 12 volt charger to charge 2.6 volt batteries. The 2.6 volt batteries will become hot, very quickly, and explode.
You would need a 24 volt charger. Connect them in parallel and you can charge them both with a 12 volt charger. Or disconnect them and charge each one separately.
A group of ten (10) batteries composed of 6 Volt and 12 Volt types will have six (6) each, 6 Volt and four (4) each 12 Volt batteries. The contributing voltages will be 6x6 and 12x4 for a total of 84 Volts.
No, since in series they are 24 volts so you need to charge each one independently with the 12 volt charger. This may be done disconnected or leave them connected and put the charger on the + - of the same battery.
No you cannot.
No.
A 10 amp charge will only output 10 amps and 12 volts. So, if you want to charge thee 12 volt batteries hooked in series you will have to disconnect the positive cable from each battery and charge then individually. You cannot charge three 12 volt batteries hooked in series. That requires a 36 volt charger.
Twelve volt batteries contain a series of 6 cells in the series.