Yes. The larger capacity means that it will deliver charge for (very slightly) longer than the other one.
Not really. 6000 mah means the battery has a capacity of 750 (6000 / 8) ma for 8 hours, while 7800 mah means the battery has a capacity of 975 (7800 / 8) ma for 8 hours.
Yes, but only if the power supply design of the laptop allows it, because the charge controls are dependent on the battery. Ask the manufacturer first.
No reason why not. So long as the physical size of the battery matches, and the voltage it delivers is the same - you should be able to replace it with the higher mAh battery.
It usually means an upgrade to a 9 cell battery with (theoretically) double the usage time, but that obviously isn't an exact science, but it is a decent rough guide
Sure, if they have the same voltage.
The number that you refer to is the ampacity of the battery. The higher the number the longer the battery will operate in the device. As long as the voltage output of the two batteries are the same it will not ruin your laptop.
can use 1400mah battery to replace 760 mah
Yes and no. The higher capacity battery will last longer, but you need to consider the charger. It depends on the design of the circuit.
mAh stands for milli ampere hour and it is a measurement of how many milli amps of current a battery is capable of producing in one hour. Yes you can substitute a battery with a higher mAh current rating provided you use the same battery voltage.
Not a good idea. It will work but not as long as the 1000 mAh battery.
Yes as long as both the 2450 mAh battery and 600 mAh battery have the same voltage. The larger one will just last longer and take longer to charge up (I am assuming these are the solar powered type lights).
No, a 1000 mAh battery should not replace a 400 mAh battery in solar lights unless the system is designed to handle the higher capacity. Using a battery with a significantly higher capacity than what the system is designed for can potentially damage the circuitry and reduce the efficiency of the lights. It's best to stick with the recommended battery capacity for optimal performance.