If I run the command below on any Linux computer from a terminal, I get the result shown below.

If I run the command correctly, I get the result shown below which is expected as it is EFI.

Anyhow, moot point as post 6 clearly shows a Legacy/MBR install. If you ran the command below which you show in your post above, you left out part of the command, the 2nd option.

I'm not sure what you are trying to accomplish. Your original post indicates you want advice on re-installing windows and you asked whether that would create any problems. Why are you re-installing Grub? Did you original Mint not boot? Did your windows not boot? Your post refers to moving files/folders from windows so it would appear you have/had a functioning windows OS? Did you now re-install windows?

it will not show you a grub, but your OSes pick one, there should be a list of optional boot "formats" for a lack of a better way to put it. if you see one that says your disto and the partition you have it installed on pick that one and hit enter.

This problem always is happening with my customers. Installing Windows does not see Linux but installing Linux makes a new grub and you can dual boot.

The latest case is a man who has Windows XP and wants to install Windows 10 but save his programs. So my advice is to install Linux Mint 19.1 which I gave him on a yumi stick with Windows 10 and Mint 19.1 and gparted.

I suggest he then copies all his data and programs over the Linux desktop from the Window to a folder in Mint.
Then with gparted format the NTFS partition of the Windows XP then install Windows 10 from the Yumi.
Then of course he can only boot into Windows so rather than installing a second Mint in order to find the first mint and copy the files over to the new Windows 10.
So he uses super grub 2 from the yumi to boot to the Linux.

Now the problem is how to install the grub that will have Linux and Windows on.

The question is can he just do a grub update and everything is back

Bear in mind I suggested to reformat the larger NTFS Windows XP and not the smaller one thinking that would still contain the grub.

What do you think?

That is my experience also but with windows 10 (not sure about earlier versions), immediately after the EULA page, there is an option to select regular/normal install or Custom install. If you select Custom install, it will show the drives with the windows nomenclature. In my situation, it was labelled drive 0 partition 3. Format the primary partition as ntfs and mark it as active for the install.

I would think it would be better to first create an ntfs partition a little larger than the data you want to copy rather than copy it to a Linux filesystem.

If you create a separate ntfs partition prior to install on which to copy the data from the old xp, windows will recognize that partition and you won't need to bother with copying from Mint. If you want that data all on the same partition as the windows OS, you can simply copy it there after the windows install.

If you are able to boot the old Mint using SuperGrubDisk, the instructions posted above to install it to /dev/sda (if that is the correct drive) and then doing a sudo update-grub should create a new Grub boot menu listing both systems. If you don't run update-grub, a new grub.cfg file will not be created and it will be using the old one which probably had an entry for xp and won't boot windows 10.

Grub files should not be on an ntfs partition. Given the size of the partition shown in your earlier post and below, it appears to be a windows boot partition. Partition 3 should be the OS partition, 130GB in size.

post hast, as @yancek stated, I'd get a big external or internal 2.5" used as external, and copy, move the entire windows (mostly users home) onto it, then sift through it later. spiting the Linux OS this is the best way because of situations just like this. you find yourself wanting to install a 3rd Linux, rather than just formatting the same one and installing a fresh mint in its place, if it is separated, then what you have in your home is safe because all that is needed is to add the mount point to it, and tell the installer not to formate it.

Windows install has a expert mode as stated, use that to point it to which partitions you want it installed on, there installer is little difference then using a gui Linux installer, it has the same options, delete, create partitions, format which partitions, mount points you tell it to mount to, etc...

I give windows a chunk of partition however xGB big you want yours, very min is 30GB w/o updates or much room left to install much of anything, an app or two, then tell it to use that one, and let it slice it up however it sees fit for its restore and hibernate partitions.

this is if you can now access your windows partitions, you can even use a usb live Linux OS to do all of this moving your windows data somewhere safe then wipe your hdd keeping your home partition in Linux if you want to. then re-establish your hdd to how you need it to be, windows install first, next Linux, done. Main issue is having an extra hdd big enough to store your data. or evaulate what you can lose because you can get it back, ie things you've downloaded off of someone elses sight, dropbox or some other sort of back up keep my important stuff somewhere else system too is a good idea to look into.