If you just cut-paste or copy-paste using Explorer, files & folders shall get copied to the destination but the file attributes will not be preserved. If you want to preserve the file attributes & also review the logs for success/failure etc (since you might have bulk of files), you can use built-in command line ROBOCOPY with suitable parameters. robocopy
It will also log status so that you can review and manually take decisions after copying, if the need be.
In case by Documents, Photos, Downloads you are referring to the Libraries available by same name in the explorer left pane, then you can simply move them to another location and all data will get automatically moved. Right click the Library – Properties - Location, click Move and follow the instructions.
What I generally do is first copy using ROBOCOPY to the new destination, then point Libraries to the new destination folder, this way file attributes are preserved and Libraries also get remapped.
If your new 1 TB HDD is initialized as GPT, you can create up to 128 Partitions on it of your choice.
