Apple may have an extended warranty for your system I would start there. If not, review the IFIXIT guide on replacing the HD it's a bit of work and you do need the proper tools as you can kill your display if you're not careful! You may end up wanting Apple or someone with the skills & tools to do it for you.
You'll need to break the fusion drive set before you remove the HD if you are planning on still trying to use the drive externally. The systems firmware & OS know the drive by its GUID drive ID so hooking it up externally can create confusion when you have a new drive hooked up internally. You don't need to worry about the SSD.
Are you sure your drive is going? It maybe you just don't have enough free space on it (1/4 ~ 1/3 free) and/or the drive is fragmented. While the OS does try to not fragment things it can't really solve this when you are upgrading apps & OS as they tend to reuse the same locations and need more space as well. How about creating a bootable external drive (USB thumb drive 16GB or larger) so you can run Disk Utility to check the drive for any errors first (repair both the permissions & disk). Then download this app or something like it: Disk Doctor to clean out the logs & caches. Lastly I would get this: Drive Genius it will defrag the HD and other useful tools.