Address of video memory (0xB8000), who is mapping video memory to this address?
The routine which is copying the data from the address and putting to the screen, Is it a processor inbuilt function (Is this driver comes with the processor)?
What happens when you write to the address:
That area of the address space is not mapped to RAM, instead it gets sent across the system bus to your VGA card. The BIOS set this up with your VGA card at boot time (Lots of address ranges are memory mapped to various devices). No code is being executed on the CPU to plot the pixels when you write to this area of the address space. The VGA card receives this information instead of your RAM and does this itself.
If you wanted you could look BIOS functions calls and have it reconfigure the hardware so you could plot pixels instead of place characters at the video address instead. You could even probe it to see if it supports VESA and switch to a nice 1280*768 32bpp resolution. The BIOS would then map an area of the address space of your choosing to the VGA card for you.
More about the BIOS:
The BIOS is a program that comes with your motherboard that your CPU executes when it first powers up. It sets up all the hardware, maps all the memory mapped devices, creates various useful tables, assigns IO ports, hooks interrupts up to a bunch of routines it leaves in memory. It then loads your bootsector from a device and jumps to your OS code.
The left behind routines and data structures enable you to get your OS off the ground. You can load sectors off a disk, write text to the screen, get information about the system (Memory maps, ACPI tables, MP Tables .etc). Without these routines and data structures, it would be a lot harder if not impossible to make an acceptable bootsector and have all the information about the system to build a functional kernel.
However the routines are dated, slow and have very restrictive limitations. For one the routines left in memory are 16bit real mode code, so as soon as you switch to 32bit protected mode you have to switch back constantly or use VM86 mode to access them (Completely unaccessible in 64bit mode, Apparently emulating the instructions with a modified linux x86emu library is an option though). So the routines are generally very slow. So you will need to write your own drivers from scratch if you move away from real mode programming.