Does every Linux OS need one such root partition?
Yes, that is the designation of the partition on which you install the main parts of the operating system.
Because Linux is capable of having different parts of its operating system on different partitions, the user is given the option to specify more than one partition to be used during the install.
The most popular use of a second partition is for the /home part of the operating system.
This is where all the user data and configuration is stored.
So if you have two partitions that you can use for an installation, it is common to put / on one and use the second for /home.
This set up has advantages .... it allows for a physical separation of the user data from the OS, and so if the OS has to be reinstalled the / partition can be completely wiped without deleting any user data which is on the second partition under /home
The simplest install is to use one partition .... selected as / ........ and ensure that no other selections are made for other partitions. That will ensure that the complete OS, including user data is placed on a single partition ....... which is what you appear to desire at this time.
So, in your case, when installing PCLinuxOS, you would select sda3 as the / partition, and have no other partition selected.
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Grub manages the boot selections as presented to the user, and allows multiple OSs to be bootable through the selection screen.
The MBR is a particular physical section of the HDD.
It is in that section that the boot manager is installed, to allow the HDD to be bootable.
In addition, each Partition has a special section, which acts in a similar manner to the MBR, but for the partition only.
If the overall HDD booting is not to be interfered with, Grub can be installed to the partition's boot sector.
With that arrangement the 'master' Grub on the MBR can be set to link to Grub installs on partition boot sectors.
So you could have one master Grub installation on the MBR, and 20 or more grub installations on partition boot sectors.
Now you can just imagine what the selection screen might look like if you had 20 installs, each of which having 5 boot options for each individual OS installed.
The user would have to select from 100 boot options.
Installing grub to the boot sector of the partitions, and using the master Grub install to link to each of the 20 boot sector installs, gives the user 20 boot options to choose from ..... and each can be named simply with the OS name.
This makes it much easier for the user to make the selection.
Of course with only one or two OS installs it is not necessary to use this scheme, but it is available if required.
So it seems you wish to place PCLinuxOS on
sda3 so select that partition as /
When, at the end of the installation, you get to select the options for the Grub install, you can select either
sda which will cause PCLinuxOS to become the master Grub on the MBR, or, if you wish to retain a different OS controlling the master Grub, you would put the PCLinuxOS Grub on
sda3 (the boot sector of the partition).
If it is put on
sda3, then you will need to make whatever edit is required to the master Grub to allow it to present the PCLinuxOS boot option to the user.
I hope I did not make things more confusing .....