Grub is a bootloader (stands for GRand Unified Bootloader). If you don't install it, you need to make a bootdisk (setup may ask you to do this) or you will not be able to boot your Linux system. If you do install GRUB it may, depending on your configuration, overwrite your existing Windows bootloader. GRUB can boot several operating systems easily; if you want to use Windows bootloader instead (and load your Linux with it too), you'll need to do some extra configuration (install GRUB not to the MBR but to the beginning of a partition, then create an image of it and use that with Windows bootloader).
Web browsers? Well, they are the programs you usually use to browse the internet - that is, load some webpage like www.linuxquestions.org
and so on. Other widely used web browsers are Opera, Internet Explorer, Mozilla (suite), ... you may install as many as you like, or just select one you prefer most.
It is possible to install Linux from a live-cd like Knoppix, but Knoppix (for example) is targeted as a live-cd only, and it's hardware installation is not something I'd recommend. Usually live-cds are not meant for harddisk installation, and the procedure may be problematic during or after the installation. Better stick to the distributions that are meant to be installed on harddisk - some of them do offer you a "live-cd" before you install, like Ubuntu for example (normal Ubuntu is a live-cd that contains an installer also).