Backing up important personal files such as photos, videos, documents, projects, etc is as easy as coping them from one drive to another. So if you don't have anything you need from your SSD then you won't need to backup anything.
I assume you're talking about booting from your installation media (DVD, USB). It won't prompt you to format anything, however when you start the installation process you'll have to select a storage device in order to install Windows. Then you'll have the option to manually reformat and repartition that drive as you see fit.
If you already have a retail product key, then you won't need to by Windows again. All you'll need to do is install the same version and use your product key. However, if that Windows is OEM (original equipment manufacturer - the OS came with a pre-build computer/laptop) then you won't be able to use that product key with the new system.
The HDD won't have to be reformatted. If it has no system files and/or partition on it, it is OK as it is. However if you have installed programs and/or games on it, some of them might not run properly with the new Windows installation so you'll need to reinstall them. I'd recommend that you have all other drives (besides the SSD you're installing Windows to) disconnected from the motherboard during the Windows installation process, in order to avoid future issues with the OS.
What's the Windows version you're using? 7, 8, 10?
Keep me posted and don't hesitate to ask if you have more questions, or if I haven't explained something properly.