You can. But the Windows installation does not put an entry into it's boot menu, so you have to manually copy a boot sector, and modify the boot menu so you can boot Linux. Linux distributions expect that you may want to dual-boot, so they detect Windows and set up an option for it automatically. For convenience's sake, it is far easier to install Windows first.
Yes, install Windows first, then whichever distribution of Linux you want second.
Boot with Windows install disk and follow instructions.
If you would like to install it ON TOP of Windows: Install a virtual machine program (ex. Virtualbox, VMware) Install Linux inside of virtual machine Install it along side (or overwrite) Windows: Reboot computer with Linux install CD/DVD in the disk drive and follow the instructions.
Yes Ubuntu-linux offers the "install along side windows" option.
Yes.
Yes. All you have to do is give Linux its own partition.
Linux is not an operating system by itself. Just like you cannot install Windows you have to install Windows XP or Windows Vista. You can use the website in related links to find a list of active Linux Distributions. If I could recommend one I would recommend Linux Mint because it is easy to use.
Have a look at WUBI (search Google) to install Ubuntu as a file, without making any changes to your Windows 8 hard-drive. To remove WUBI, simply use Windows utility to uninstall programs. Or, create a separate partition on the Windows hard-drive and install Linux (or which ever distro you wish to use) on to the new partition. Remember to first backup important files onto an external storage device. Or, download and burn a Linux distribution with an ISO extension onto a CD and use as a Live Disk. If you then intend to install Linux, you will be given the choice to either install as a dual-boot with Windows by installing Linux alongside Windows, or wiping Windows and letting Linux use all the hard-drive.
Re-install the operating system or install Linux.
No.
Yes, you can. It's called dualbooting. I guess with Linux you mean a Linux Distribution like Ubuntu? Check the related link if you want to know how.
Yes. There is a Linux port of Virtualbox and it runs Windows as well as any version of VB.