If I reset my computer to factory settings will I have to re-enter the Windows 10 key and will a partitioned drive be reset?

if it came with 10, then only the c: drive is usually re-built as it checks the other exist and doesnt recreate them. you will only need to re-enter the key if thats what you did last time. if its an upgrade version it will most likely want the original OS disk, and the new w10 key as well.

No and No

If you reset to factory you won't need a key as the details are sent to M$ servers and the activation occurs automatically. If you leave the drive partitions intact they will remain unchanged, but you can change this with a custom install.