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.
Yes. The larger capacity means that it will deliver charge for (very slightly) longer than the other one.
It's not a question about "better", it's about what's most important to you - weight/size or runtime. The 4800 mAh battery will last longer, but will probably also be bigger/heavier. More to carry around. The 3600 mAh will last a bit shorter, but will be smaller and lighter. You have to decide what you prefer.
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.
The battery with the larger mAh rating will last longer that the battery with the smaller mAh number will last in the same application.
Only if the battery is rated at 11.66V. mAh / 1000 => Ah (4800 mAh = 4.8 Ah) Ah * V => Wh (4.8 Ah * 11.66 V = 55.97 Wh)
In general, no. The charger is designed for a specific battery profile, and it might not be able to properly charge and/or monitor the amount of charge if you put in a different battery.
You simply divide the MAH of your battery the MAH of your charger. For example my battery is 1500 MAH and my charger is 250 MAH. 1500/250=6 which means I have to charge my battery for six hours.
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.
Sure, if they have the same voltage.
Milliamps Hour (mAh) is important because it's the easiest way to distinguish the strength or capacity of a battery. The higher the mAh, the longer the battery will last. Batteries with different mAh ratings are interchangeable. If your battery is rechargeable then the mAh rating is how long the battery will last per charge. Milliamps Hour is 1/1000th of a Amp Hour, so a 1000mAh = 1.0Ah Think of a cars gas tank. Voltage is how much gas is being used, and mAh is the size of the gas tank. The bigger the gas tank (mAh) rating the longer the device will run. If your battery is rechargeable, then think of the gas tank as refillable (rechargeable).