Can ATI Radeon 7770 be installed on hp pavilion g6?

Answer 1

In most cases, you cannot change a laptop's graphics card.

For nVidia mobile GPUs, they are separate from the CPU, but cannot be changed if they are directly soldered to the laptop's board.

For Intel HD graphics GPUs, they are normally integrated with the CPU, so getting a better CPU which is compatible with your laptop's socket, and ideally has same heat output (TDP), may have a better GPU, although the performance difference shouldn't be very drastic.

For ATI/AMD mobile GPUs, this varies for each laptop, some are integrated, some are separate, you need to check. AMD designates separate GPUs as "discrete graphics".