1. No reason it should not.
Based on this image, you should just need a bracket. They have them online, but they are somewhat expensive:
You can get away with foam + screws from a local shop, but it is not ideal especially if you move the notebook around a lot.
3-7. Ideally, using a clean 8.1 iso is ideal, but finding one is getting more difficult.
Try the burn recovery software, but make sure you unplug the 1TB before starting the install.
If that fails, look into cloning software. Since you are buying a Samsung you can use Samsung Data Migration(or if you decide to get another drive, there are free programs like Macrium Reflect).
Note: 1) Backup any important data
2) Unplug the 1 TB for first boot after cloning. You don't want any conflicts at the beginning or you could get a BSOD/windows recovery message. After first boot, just restart once to ensure computer still boots up, then shutdown and plug in the 1TB back in.
3) Read the guides online for these software, Make sure to copy all partitions and pay attention to which drive you are cloning too.
3) These software can clone a from large drive to a smaller driver, but I think it works best when go from small to big. If you 1TB is full, clean some stuff off or move it temporarily to another computer/external driver/online backup source.